# 5

 ← 4 5 6 →
Cardinalfive
Ordinal5th
(fifth)
Numeral systemquinary
Factorizationprime
Prime3rd
Divisors1, 5
Greek numeralΕ´
Roman numeralV, v
Greek prefixpenta-/pent-
Latin prefixquinque-/quinqu-/quint-
Binary1012
Ternary123
Octal58
Duodecimal512
Greekε (or Ε)
Arabic, Kurdish٥
Persian, Sindhi, Urdu۵
Ge'ez
Bengali
Punjabi
Chinese numeral五,伍
Devanāgarī
Hebrewה
Khmer
Telugu
Malayalam
Tamil
Thai

5 (five) is a number, numeral and digit. It is the natural number following 4 and preceding 6, and is a prime number. It has attained significance throughout history in part because typical humans have five digits on each hand.

## In mathematics

Five is the third prime number.[1] Since it can be written as 221 + 1, five is classified as a Fermat prime;[1] therefore, a regular polygon with 5 sides (a regular pentagon) is constructible with compass and an unmarked straightedge. Five is the third Sophie Germain prime,[1] the first safe prime, the third Catalan number,[2] and the third Mersenne prime exponent.[3] Five is the first Wilson prime and the third factorial prime, also an alternating factorial.[4] Five is the first good prime.[5] It is an Eisenstein prime with no imaginary part and real part of the form 3n − 1.[1] It is also the only number that is part of more than one pair of twin primes. Five is a congruent number.[6]

Five is conjectured to be the only odd untouchable number[7] and if this is the case then five will be the only odd prime number that is not the base of an aliquot tree.

Five is also the only prime that is the sum of two consecutive primes, namely 2 and 3, with these indeed being the only possible set of two consecutive primes.

The number 5 is the fifth Fibonacci number, being 2 plus 3.[1] It is the only Fibonacci number that is equal to its position. Five 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), ... ( 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.[8]

5 is the length of the hypotenuse of the smallest integer-sided right triangle.

In bases 10 and 20, 5 is a 1-automorphic number.

Five is the second Sierpinski number of the first kind, and can be written as S2 = (22) + 1.[9]

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.

There are five Platonic solids.[10][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

Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
5 × 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 ÷ x 5 2.5 1.6 1.25 1 0.83 0.714285 0.625 0.5 0.5 0.45 0.416 0.384615 0.3571428 0.3
x ÷ 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
5x 5 25 125 625 3125 15625 78125 390625 1953125 9765625 48828125 244140625 1220703125 6103515625 30517578125
x5 1 32 243 1024 3125 7776 16807 32768 59049 100000 161051 248832 371293 537824 759375

In the powers of 5, every power ends with the number five and from 53, if the exponent is odd, then the hundreds digit is 1; instead, if it is even, the hundreds digit is 6.

In fifth powers, n5 ends in the same digit as n.

## Evolution of the Arabic digit

The evolution of the modern Western digit for the numeral 5 cannot be traced back to the Indian system, as for the digits 1 to 4. The Kushana and Gupta empires in what is now India had among themselves several different forms that bear no resemblance to the modern digit. The Nagari and Punjabi took these digits and all came up with forms that were similar to a lowercase "h" rotated 180°. The Ghubar Arabs transformed the digit in several different ways, producing from that were more similar to the digits 4 or 3 than to 5.[11] It was from those digits that Europeans finally came up with the modern 5.

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

## Science

### Biology

• There are generally considered to be five senses.
• Almost all amphibians, reptiles, and mammals which have fingers or toes have five of them on each extremity.[18]

## Religion and culture

### Hinduism

• The god Shiva has five faces[20] and his Mantra is also called Panchakshari (Five Worded) mantra.
• The goddess Saraswati, goddess of knowledge and intellectual is associated with Panchami or number 5.
• There are five elements in this universe: Dharti, Agni, Jal, Vayu evam Akash (Earth, Fire, Water, Air and Space respectively).
• The most sacred tree in Hinduism has 5 leaves in every leaf stunt.
• Most of the flowers have 5 petals in them.
• The epic Mahabharata revolves around the battle between Duryodhana and his 99 other brothers and the 5 pandava princes -Dharma, Arjuna, Bhima, Nakula and Sahadeva.

### Discordianism

• 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.

### Sikhism

• 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's Gurmukhi script. They are: kesh (unshorn hair), kangha (the comb), kara (the steel bracelet), kachhehra (the soldiers shorts), and kirpan (the sword) (in Gurmukhi: ਕੇਸ, ਕੰਘਾ, ਕੜਾ, ਕਛਹਰਾ, ਕਿਰਪਾਨ).[28] Also, there are five deadly evils: kam (lust), krodh (anger), moh (attachment), lobh (greed), and ankhar (ego).

## Art, entertainment, and media

Stations
Series

### Literature

• The Famous Five is a series of children's books by British writer Enid Blyton
• The Power of Five is a series of children's books by British writer and screenwriter Anthony Horowitz
• The Fall of Five is a book written under the collective pseudonym Pittacus Lore in the series Lorien Legacies
• The Book of Five Rings is a text on kenjutsu and the martial arts in general, written by the swordsman Miyamoto Musashi circa 1645
• Slaughterhouse-Five is a book by Kurt Vonnegut about World War II[69]

## Sports

• The Olympic Games have five interlocked rings as their symbol, representing the number of inhabited continents represented by the Olympians (Europe, Asia, Africa, Australia and Oceania, and the Americas).[70]
• In AFL Women's, the top level of women's Australian rules football, each team is allowed 5 "interchanges" (substitute players), who can be freely substituted at any time.
• In baseball scorekeeping, the number 5 represents the third baseman's position.
• The number 5 is used to represent the position of center.
• Each team has five players on the court at a given time. Thus, the phrase "five on five" is commonly used to describe standard competitive basketball.[71]
• The "5-second rule" refers to several related rules designed to promote continuous play. In all cases, violation of the rule results in a turnover.
• Under the FIBA (used for all international play, and most non-US leagues) and NCAA women's rule sets, a team begins shooting bonus free throws once its opponent has committed five personal fouls in a quarter.
• Under the FIBA rules, A player fouls out and must leave the game after committing five fouls
• Five-a-side football is a variation of association football in which each team fields five players.[72]
• In ice hockey:
• A major penalty lasts five minutes.[73]
• There are five different ways that a player can score a goal (teams at even strength, team on the power play, team playing shorthanded, penalty shot, and empty net).[74]
• The area between the goaltender's legs is known as the five-hole.[75]
• In most rugby league competitions, the starting left wing wears this number. An exception is the Super League, which uses static squad numbering.
• In rugby union:

## Technology

• 5 is the most common number of gears for automobiles with manual transmission.[77]
• In radio communication, the term "Five by five" is used to indicate perfect signal strength and clarity.[78]
• 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).[79]
• On most telephones, the 5 key is associated with the letters J, K, and L,[80] 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.[81]
• The resin identification code used in recycling to identify polypropylene.[82]
• A pentamer is an oligomer composed of five subunits.

## Miscellaneous fields

The fives of all four suits in playing cards

Five can refer to:

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87. Roads, United States Congress Senate Committee on Public Works Subcommittee on (1970). Designating Highway U.S. 50 as Part of the Interstate System, Nevada: Hearings, Ninety-first Congress, First Session; Carson City, Nevada, October 6, 1969; [and] Ely, Nevada, October 7, 1969. U.S. Government Printing Office. p. 78.
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93. Hargrove, Julia (2000-03-01). John F. Kennedy's Inaugural Address. Lorenz Educational Press. p. 24. ISBN 978-1-57310-222-3. The five permanent members have a veto power over actions proposed by members of the United Nations.
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95. Hand, Seven Star (2010-09-17). Finishing the Mysteries of Gods and Symbols: Volume 0. Seven Star Hand. p. 90. ISBN 978-1-257-93419-5. ...the pentacle as a five-pointed star (pentagram) ...
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