5 | |||||||||
---|---|---|---|---|---|---|---|---|---|

Numbers 0 - 99 | |||||||||

0 | 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 | 26 | 27 | 28 | 29 |

30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 |

40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 |

50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 |

60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 |

70 | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 |

80 | 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 |

90 | 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 |

**5 (five)** is a positive integer following 4 and preceding 6. Its ordinal form is written "fifth" or "5th".

## Contents

## Properties

- 5 is an odd prime number. Since 10 is a multiple of 5, divisibility by 5 can be easily tested in the decimal system — multiples of 5 always end in 0 or 5. 5 is a Fermat prime: 2
^{21}+ 1 = 5. - A 5-sided star is known as a pentagram.
- 5 is the only known odd untouchable number.
- The base five numeral system is called quinary or pental.

## In googology

- Some googologisms based on 5 are superpent, googolquinplex and quintoogol. 5 is the length of the Goodstein sequence starting with 3, which goes 3, 3, 3, 2, 1.
- In Greek-based number naming systems, 5 is associated with prefix penta-, and with prefix quinti- in Latin systems.
- Flan number 5 version 2 (or フラン数第五形態改二 in Japanese) is equal to 5.

### Googological functions returning 5

- Goodstein function: \(G(3)=5\)
- Weak Goodstein function: \(g(3)=5\)
- Laver table: \(q(3)=5\)
- Weak tree function: \(\text{tree}(2)=5\)
- Friedman's circle theorem: \(\text{Circle}(1)=5\)
- simple subcubic graph number: \(\text{SSCG}(1)=5\)

## As a cash denomination

Some currencies, such as the euro and the United States dollar, have banknotes with this number in the denomination.

Some currencies, such as the Czech koruna, the Israeli new shekel (shekel-wise and formerly Agorot-wise) and the Russian ruble, have coins with this number in the denomination.

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