Five

Five is the third smallest prime number, the next is seven. Because it can be written as 2^(2^1)+1, five is classified as a Fermat prime.

Five is a factor of 10, so fractions with 5 in the denominator do not yield infinite decimal expansions, unlike most other primes.

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.

The Roman numeral for five is V.

In Cantonese, five sounds like the word "not" (symbol 唔). So when five appears in front of a lucky number, e.g. 58, the result is considered unlucky.

Giving five refers to slapping hands with someone as a sign of approbation.

Five is also:

• the number of sides in a pentagon
• the number of Platonic solids.
• the number of dots in a quincunx
• the number of musicians in a quintet[?].
• the number of permanent members with veto power on the UN Security Council.
• almost all amphibians, reptiles, birds and mammals which have fingers or toes have five of them on each extremity.

For the UK TV channel Five, see Five (TV).