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Five (5) is the natural number following four and preceding six.

 Table of contents 1 Five in mathematics 2 Five in numbering systems 3 Five in various cultures 4 Five is also 5 Five in music 6 Other usages 7 See also

## Five in mathematics

• 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 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.
• The number 5 is a Fibonacci number, being 2 plus 3. The next Fibonacci number is 8.
• Five is a factor of 10, so fractions with 5 in the denominator do not yield infinite decimal expansions, unlike most other primes. When written in the decimal system, all multiples of 5 will end in either 5 or 0.
• 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.
• Five is the answer to the question asked at the very end of the mathematics quiz show in the movie Little Man Tate. (Our young protagonist blurts out the answer, but the host mishears it as being the answer from the contestant to whom the question is posed, and declares him the winner.)

## Five in various cultures

• There are five basic "pillars" of Islam.
• Islamic people pray to Allah five times a day (Mohammed was said to have bargained it down with Allah from fifty).
• According to the Maya mythology, we are now living in the Fifth World.
• In the Oriental 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, rather than from the planets.
• 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.

## Other usages  