5 (number)

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This article is about the number five. For the year AD 5, see 5. For other uses of 5, see 5 (disambiguation) and The Five (disambiguation).
4 5 6
−1 0 1 2 3 4 5 6 7 8 9
Cardinal five
Ordinal 5th
Numeral system quinary
Factorization prime
Divisors 1, 5
Roman numeral V
Roman numeral (unicode) Ⅴ, ⅴ
Greek prefix penta-/pent-
Latin prefix quinque-/quinqu-/quint-
Binary 1012
Ternary 123
Quaternary 114
Quinary 105
Senary 56
Octal 58
Duodecimal 512
Hexadecimal 516
Vigesimal 520
Base 36 536
Greek ε (or Ε)
Arabic ٥,5
Persian ۵
Urdu ۵
Chinese numeral 五,伍
Korean 다섯,오
Devanāgarī (panch)
Hebrew ה (Hey)

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

In mathematics[edit]

Five is the third [[prime 221+1, five is classified as a Fermat prime; therefore a regular polygon with 5 sides (a regular pentagon) is constructible with compass and unmarked straightedge. 5 is the third Sophie Germain prime, the first safe prime, the third Catalan number, and the third Mersenne prime exponent. Five is the first Wilson prime and the third factorial prime, also an alternating factorial. Five is the first good prime. 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 a congruent number. 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 fifth 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), ... (OEISA030452 lists Markov numbers that appear in solutions where one of the other two terms is 5). Whereas 5 is unique in the In bases 10 and 20, 5 is a 1-automorphic number.

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=(22)+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 Sn 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.[1]

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, unlike expansions with all other prime denominators, 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.

List of basic calculations[edit]

Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
5 \times x 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
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{714285} 0.625 0.\overline{5} 0.5 0.\overline{45} 0.41\overline{6} 0.\overline{384615} 0.\overline{357142} 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 14 15
5 ^ x\, 5 25 125 625 3125 15625 78125 390625 1953125 9765625 48828125 244140625 1220703125 6103515625 30517578125
x ^ 5\, 1 32 243 1024 3125 7776 16807 32768 59049 100000 161051 248832 371293 537824 759375

Evolution of the glyph[edit]


The evolution of the modern Western glyph for five cannot be neatly traced back to the Indian system as for the numbers 1 to 4. The Kushana and Gupta empires in what is now India 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 are similar to a lowercase "h" rotated 180°. The Ghubar Arabs transformed the glyph in several different ways, producing glyphs that were more similar to the numbers 4 or 3 than to the number 5.[2]

It was from those characters that Europeans finally came up with the modern 5, though from purely graphical evidence, it would be much easier to conclude that the modern symbol came from the Khmer. The Khmer glyph develops from the Kushana/Ândhra/Gupta numeral, its shape looking like the modern version with an extended swirled 'tail' [3]

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 TextFigs256.png.




  • Perception is conceived to occur through five senses.
  • Almost all amphibians, reptiles, and mammals which have fingers or toes have five of them on each extremity.[4]


Religion and culture[edit]

  • 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 four fingers and one thumb, is used as a protective amulet by Jews; that same symbol is also very popular in Arabic culture, known to protect from envy and the evil eye.
  • 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 (ਕ) in the Punjabi language/Gurmukhi Script. They are: Kesh (unshorn hair), Kangha (the comb), Kara (the steel bracelet), Kachhehra (the soldiers shorts), and Kirpan (the sword) [in Gurmukhi Script: ਕੇਸ, ਕੰਘਾ, ਕੜਾ, ਕਛਹਰਾ, ਕਿਰਪਾਨ]. Also, there are five deadly evils: Kam (lust), Krodh (anger), Moh (attachment), Lobh (greed), and Ankhar (ego).
  • In Discordianism, 5 is seen as a very important number. This is demonstrated in the Law of Fives, as well as in the Pentabarf, which contains five rules.
  • Each page of the Principia Discordia —the primary religious document in Discordianism— is labeled with five digits.



Film and television[edit]




5 as a resin identification code, used in recycling.
  • 5 is the most common number of gears for automobiles with manual transmission.
  • In radio communication, the term "Five by five" is used to indicate perfect signal strength and clarity.
  • 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).
  • On most telephones, the 5 key is associated with the letters J, K, and L, but on some of the BlackBerry phones, it is the key for G and H.
  • The Pentium, coined by Intel Corporation, is a fifth-generation x86 architecture microprocessor.
  • The resin identification code used in recycling to identify polypropylene.
  • A pentamer is an oligomer composed of five sub-units.

Miscellaneous fields[edit]

St. Petersburg Metro, Line 5

Five can refer to:

The fives of all four suits in playing cards

See also[edit]


  1. ^ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 61
  2. ^ 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
  3. ^ Ifrah, Georges (1998). The universal history of numbers : from prehistory to the invention of the computer. translated from the French by David Bellos ... [et al.] London: Harvill Press. ISBN 978-1-86046-324-2. 
  4. ^ Kisia, S. M. (2010), Vertebrates: Structures and Functions, Biological Systems in Vertebrates, CRC Press, p. 106, ISBN 9781439840528, The typical limb of tetrapods is the pentadactyl limb (Gr. penta, five) that has five toes. Tetrapods evolved from an ancestor that had limbs with five toes. ... Even though the number of digits in different vertebrates may vary from five, vertebrates develop from an embryonic five-digit stage. 

External links[edit]