5

	5
	Template:Numbers (digits)
Cardinal	5 ; five
Ordinal	5th ; fifth
Numeral system	quinary
Factorization	prime
Divisors	1, 5
Roman numeral	V
Roman numeral (Unicode)	Ⅴ, ⅴ
Arabic	٥
Arabic (Urdu)	۵
Ge'ez	፭
Bengali	৫
Chinese numeral	五，伍
Devanāgarī	५
Hebrew	ה (He)
Khmer	៥
Thai	๕
prefixes	penta-/pent- (from Greek) quinque-/quinqu-/quint- (from Latin)
Binary	101
Octal	5
Duodecimal	5
Hexadecimal	5
Vigesimal	5

This article discusses the number five. For the year 5 AD, see 5. For other uses of 5, see 5 (disambiguation).

5 (five) is a number, numeral, and glyph. It is the natural number following 4 and preceding 6.

Mathematics

Five is between 4 and 6 and is the third prime number, after 2 and 3, and before 7. Because it can be written as 2^(2^1)+1, five is classified as a Fermat prime. 5 is the third Sophie Germain prime, the first safe prime, and the third Mersenne prime exponent. Five is the first Wilson prime and the third factorial prime, also an alternating factorial. It is an Eisenstein prime with no imaginary part and real part of the form $3n-1$ . It is also the only number that is part of more than one pair of twin primes.

Five is conjectured to be the only odd untouchable number and if this is the case then five will be the only odd prime number that is not the base of an aliquot tree.

The number 5 is the 5th Fibonacci number, being 2 plus 3. 5 is also a Pell number and a Markov number, appearing in solutions to the Markov Diophantine equation: (1, 2, 5), (1, 5, 13), (2, 5, 29), (5, 13, 194), (5, 29, 433), ... (OEIS: A030452 lists Markov numbers that appear in solutions where one of the other two terms is 5). Whereas 5 is unique in the Fibonacci sequence, in the Perrin sequence 5 is both the fifth and sixth Perrin numbers.

5 and 6 form a Ruth-Aaron pair under either definition.

There are five solutions to Znám's problem of length 6.

Five is the second Sierpinski number of the first kind, and can be written as S2=(2^2)+1

While polynomial equations of degree 4 and below can be solved with radicals, equations of degree 5 and higher cannot generally be so solved. This is the Abel-Ruffini theorem. This is related to the fact that the symmetric group S_n is a solvable group for n ≤ 4 and not solvable for n ≥ 5.

While all graphs with 4 or fewer vertices are planar, there exists a graph with 5 vertices which is not planar: K₅, the complete graph with 5 vertices.

Five is also the number of Platonic solids.

A polygon with five sides is a pentagon. Figurate numbers representing pentagons (including five) are called pentagonal numbers. Five is also a square pyramidal number.

Five is the only prime number to end in the digit 5, because all other numbers written with a 5 in the ones-place under the decimal system are multiples of five. As a consequence of this, 5 is in base 10 a 1-automorphic number.

Vulgar fractions with 5 or 2 in the denominator do not yield infinite decimal expansions, as is the case with most primes, because they are prime factors of ten, the base. When written in the decimal system, all multiples of 5 will end in either 5 or 0.

There are five Exceptional Lie groups.

Numbering systems

In binary, code five is 101
In ternary, code five is 12
In quaternary, numeral system code five is 11
In quinary, five is 10; and in senary, code and all codes above (such as decimal, duodecimal and vigesimal) five is 5.
The Roman numeral for five is V, which comes from a representation of an outstretched hand.
In the Arabic alphabet, ٥‎ (hāʼ) has numerical value of 5.
In the Greek alphabet, ε (epsilon) has numerical value of 5.
In the Hebrew alphabet, ה (heh) has numerical value of 5.
In the Cyrillic alphabet, Е has numerical value of 5.
In the Glagolitic alphabet, (dobro) has numerical value of 5.
The kanji and Chinese character for five are both 五, and its formal writing in Chinese is 伍 (pinyin wǔ).

List of basic calculations

Multiplication	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15	16	17	18	19	20		21	22	23	24	25		50	100	1000
$5\times x$	5	10	15	20	25	30	35	40	45	50		55	60	65	70	75	80	85	90	95	100		105	110	115	120	125		250	500	5000

Division	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15
$5\div x$	5	2.5	$1.{\overline {6}}$	1.25	1	$0.8{\overline {3}}$	$0.{\overline {7}}1428{\overline {5}}$	0.625	$0.{\overline {5}}$	0.5		$0.{\overline {4}}{\overline {5}}$	$0.41{\overline {6}}$	$0.{\overline {3}}8461{\overline {5}}$	$0.3{\overline {5}}7142{\overline {8}}$	$0.{\overline {3}}$
$x\div 5$	0.2	0.4	0.6	0.8	1	1.2	1.4	1.6	1.8	2		2.2	2.4	2.6	2.8	3

Exponentiation	1	2	3	4	5	6	7	8	9	10		11	12	13
$5^{x}\,$	5	25	125	625	3125	15625	78125	390625	1953125	9765625		48828125	244140625	1220703125
$x^{5}\,$	1	32	243	1024	3125	7776	16807	32768	59049	100000		161051	248832	371293

Evolution of the glyph

The evolution of our modern glyph for five cannot be neatly traced back to the Brahmin Indians quite the same way it can for 1 to 4. Later on the Kushana and Gupta Indians had among themselves several different glyphs which bear no resemblance to the modern glyph. The Nagari and Punjabi took these glyphs and all came up with glyphs that look like a lowercase "h" rotated 180°. The Ghubar Arabs transformed the glyph in several different ways, coming up with glyphs that look more like 4s or 3s than 5s.^[1] It was from those characters that the Europeans finally came up with the modern 5, though from purely graphical evidence, it would be much easier to conclude that our modern 5 came from the Khmer. The Khmer glyph develops from the Kushana/Ândhra/Gupta numeral, its shape looking like a modern day version with an extended swirled 'tail' [G Ifrah, The Universal History of Numbers Template:ISBN 1-86046-324-X]

While the shape of the 5 character has an ascender in most modern typefaces, in typefaces with text figures the character usually has a descender, as, for example, in .

Science

The atomic number of boron.
The lightest atomic mass (the sum of protons and neutrons) for which no stable isotopes exist for any element.
Almost all amphibians, reptiles and mammals which have fingers or toes have five of them on each extremity.
The number of appendages on most starfish, which exhibit pentamerism.
The most destructive known tornadoes rate an F-5 on the Fujita scale.
The most destructive known hurricanes rate as Category 5 on the Saffir-Simpson scale.

Astronomy

Messier object M5, a magnitude 7.0 globular cluster in the constellation Serpens.
The New General Catalogue object NGC 5, a magnitude 13 spiral galaxy in the constellation Andromeda
The Saros number of the solar eclipse series which began on April 4, 2720 BC and ended on May 24, 1422 BC. The duration of Saros series 5 was 1298.1 years, and it contained 73 solar eclipses.
The Saros number of the lunar eclipse series which began on -2581 October 8 and ended on -1084 March 24. The duration of Saros series 5 was 1496.5 years, and it contained 84 lunar eclipses.
The Roman numeral V stands for dwarfs (main sequence stars) in the Yerkes spectral classification scheme.
The Roman numeral V (usually) stands for the fifth-discovered satellite of a planet or minor planet (e.g. Jupiter V

Religion and culture

The five sacred Sikh symbols prescribed by Guru Gobind Singh are commonly known as Panj Kakars or the 'Five Ks' because they start with letter K representing Kakka in the Punjabi language. They are: Kesh (unshorn hair), Kangha (the comb), Kara (the steel bracelet), Kachh (the soldiers shorts), and Kirpan (the sword).
There are five basic "pillars" of Islam.
Muslims pray to Allah five times a day *In Islam, particularly Shia Islam, the Panjetan or the Five Holy Purified Ones are the members of Muhammad's family including: Muhammad, Ali, Fatima, Hasan, Husayn and is often symbolically represented by an image of the Khamsa.
The Torah contains five books—Genesis, Exodus, Leviticus, Numbers, and Deuteronomy—which are collectively called the Five Books of Moses, the Pentateuch (Greek for "five containers," referring to the scroll cases in which the books were kept), or Humash (חומש, Hebrew for "fifth")
The book of Psalms is arranged into five books, paralleling the Five Books of Moses.
The Khamsa, an ancient symbol shaped like a hand with five fingers, is used as a protective amulet by Jews
According to some traditions of Maya mythology, we are now living in the Fifth World.
In East Asian tradition, there are five elements: (water, fire, earth, wood and metal). The Japanese names for the days of the week, Tuesday through Saturday, come from these elements via the identification of the elements with the five planets visible with the naked eye. Also, the traditional Japanese calendar has a five-day weekly cycle that can be still observed in printed mixed calendars combining Western, Chinese-Buddhist and Japanese names for each weekday.
In some cultures there are five cardinal directions, including the center.
In Cantonese, "five" sounds like the word "not" (symbol: 唔). When five appears in front of a lucky number, e.g. "58", the result is considered unlucky.
According to various mythologies, the universe is comprised of five classical elements: water, earth, air, fire and ether.
In Greek Orthodox Christian mysticism, the number 5 symbolizes the Holy Spirit as the bearer of all life. In the monastic tradition of Mount Athos there exists a "hymn" to the Holy Spirit composed entirely and solely of repetitions of the word "pente" (Greek for "five")
In Discordianism, 5 is seen as a very important number as demonstrated in the Law of Fives and The Pentabarf, which contains five rules. Each page of the Principia Discordia, the primary religious document in Discordianism, is also labeled with 5 digits.

Music

#5, the pseudonym of American musician Craig Jones, when performing with Slipknot
The Five is the name of a 19th century Russian Group of nationalistic composers who included César Cui, Aleksandr Borodin, Mily Balakirev, Modest Mussorgsky, and Nikolay Rimsky-Korsakov
A Perfect fifth is the most consonant harmony, and is the basis for most western tuning systems.
Modern musical notation uses a musical staff made of five horizontal lines.
Using the Latin root, five musicians are called a quintet, e.g. the Jackson Five. (In an episode of Will & Grace guest-starring Janet Jackson, she declared that 5 is a mystical number and for that reason she must have precisely 5 backup dancers).
The name of the band The Fifth Dimension implies that they are transcending beyond even the fourth dimension (time) into a new inner dimension.
There was a British boy band called 5ive.
Other bands with "five" in their name include We Five, Five for Fighting, Click Five, MC5 (short for "Motor City Five"), Ben Folds Five and the Five Man Electrical Band.
The Vogues song "Five-o'clock World" came in reference to the hours 9 to 5 (ending at 5 p.m.), which are the hours of a standard work day. There are also five working days (non-week-ends) in a week.
5 is an album by Lenny Kravitz.
5 is a song from après les dancings album by Travis Bürki.
Take Five is a famous jazz standard composed by Paul Desmond. It counts five beats per bar.
The number of completed, numbered piano concertos of Ludwig van Beethoven and Camille Saint-Saëns.
Five Minutes Of Funk is a song by New York rapper Whodini
Five Minutes Alone is a song by Heavy Metal group Pantera
Jurassic 5 is a hip hop crew whose second full length album was titled "Power In Numbers."
Maroon 5 is a pop/rock band from Los Angeles, California, that has become popular thanks to songs such as "Harder To Breathe" and "This Love." The band won the Grammy Award for Best New Artist in 2005.
In harmonics - The fifth partial (or 4th overtone) of a fundamental has a frequency ratio of 5/1 to the frequency of that fundamental. This ratio corresponds to the interval of 2 octaves + a pure major third. Thus, the interval of 5/4 is the interval of the pure third. A major triad chord when played in just intonation (most often the case in a cappella vocal ensemble singing), will contain such a pure major third.

Sports

Jason Kidd wore the number five on his jersey while playing in the NBA.

Kyle Busch's number in both the NEXTEL Cup Series and the Busch Series. Also from 1994 until 2004 NASCAR champion Terry Labonte had the number.
In Formula One, the number 5 & 6 cars traditionally belonged to the Williams team, until the end of the 1995 Formula One Season. It was most synonymous with Nigel Mansell in the late 80s and early 90s.
In professional Wrestling, if a wrestler grabs the ropes when he is in a submission hold, the attacking wrestler has up to a 5 count to break the hold until a disqualification is made. This is also the case for choking, grabbing the referee, or standing to the top of the turnbuckle. Contrary to belief, it is not a four count, as emphasized in WWE.
The number of players of a basketball team on the court at a given time.
Several players in the NBA have worn the number 5 on their jersey, including Hall of Fame caliber players Jason Kidd of the New Jersey Nets and most recently Kevin Garnett of the Boston Celtics. Bill Walton wore number 5 during the last few years of his career with the Boston Celtics.
Also used in basketball to represent the position of center.
The Olympic Games have five interlocked rings as their symbol, representing the number of inhabited continents represented by the Olympians (counting North America and South America as one continent).
The number of kyu (pupil) grades in judo
In rugby union, the number of the lock forward who usually jumps at number 4 in the line-out. It is also the number of points awarded for a try.
In rugby league, the number of the left wing, and also the number of tackles the attacking team has to score a try before the handover.
In baseball, five represents the third baseman's position.
5 is the uniform number of Hall of Fame Baseball players Hank Aaron, Luke Appling, George Brett, Lou Boudreau, Hank Greenberg, Johnny Bench, Joe DiMaggio, and Brooks Robinson.
In hockey, the area between the goaltender's legs is known as the five-hole.
Heisman Winner Reggie Bush wore the number 5 in college at the University of Southern California.
Former Collingwood Magpies captain and member of the Team of the Century Nathan Buckley wore gurnsey number 5.
The band Soilwork released the album Finger Number Five in 2003

Technology

5 as a resin identification code, used in recycling.

The resin identification code used in recycling to identify polypropylene.
In radio communication, the term "Five by five" is used to indicate perfect signal strength and clarity.
The Pentium, coined by Intel Corporation, is a fifth-generation x86 architecture microprocessor.
On most telephones, the 5 key is associated with the letters J, K, and L, but on the BlackBerry it is the key for G and H.
On almost all devices with a numeric keypad such as telephones, computers, etc., the 5 key has a raised dot or raised bar to make dialing easier. Persons who are blind or have low vision find it useful to be able to feel the keys of a telephone. All other numbers can be found with their relative position around the 5 button. (On computer keyboards, the 5 key of the numpad has the raised dot or bar, but the 5 key that shifts with % does not).
5 is the most common number of gears for automobiles with manual transmission.

Miscellaneous fields

Five is:

The number of oceans in the world.
The five senses are sight, smell, sound, touch and taste.
The five basic tastes are sweet, salty, sour, bitter and umami.
The number of the first books in the Bible: Genesis (Bereisheet בראשית), Exodus (Shemot שמות), Leviticus (Vayikra ויקרא), Numbers (Bemidbar במדבר), and Deuteronomy (Devarim דברים) also known as the Pentateuch
Pentameter is verse with five repeating feet per line; iambic pentameter was the most popular form in Shakespeare.
In the United States legal system, the Fifth Amendment to the United States Constitution can be referred to in court as "pleading the fifth", absolving the defendant from self-incrimination
The designation of an Interstate Highway that runs from San Diego, California to Blaine, Washington. In addition, all major north-south Interstate Highways in the United States end in 5.
The number of permanent members with veto power on the UN Security Council.
The number necessary to make a majority decision in the U.S. Supreme Court.
Five babies born at one time are quintuplets. The most famous set of quintuplets were the Dionne Quintuplets born in the 1930s.
In Astrology, Leo is the 5th astrological sign of the Zodiac.
Quintessence, meaning 'fifth element', refers to the elusive fifth element that completes the basic four elements (water, fire, air and earth). There is also a movie called The Fifth Element.
The number of dots in a quincunx.
The number of points in a pentagram.
The Garden of Cyrus 1658 by Sir Thomas Browne is a Pythagorean Discourse based upon the number 5.
The word "punch" comes from the Hindustani for five. Being true to the designation of punch, the drink Five Alive is named for its five ingredients.
The holy number of Discordianism, as dictated by the Law of Fives.
An informal term for the British Security Service, MI5
The typical number of members in a Super Sentai team.
Human beings and other primates have five digits on each hand as well as five toes on each foot.
There are five vowels in the English alphabet: a, e, i, o and u.

References

^ Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer transl. David Bellos et al. London: The Harvill Press (1998): 394, Fig. 24.65

Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 58 - 67

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[1] Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer transl. David Bellos et al. London: The Harvill Press (1998): 394, Fig. 24.65

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