# 5 (number)

This article discusses the number five. For the year 5 AD, see 5. For other uses of 5, see 5 (disambiguation)</center>
<tr><td>Hebrew<td>ה (He)
 Template:Numbers (digits) Cardinal 5 five Ordinal 5th fifth Numeral system quinary Factorization prime Divisors 1, 5 Roman numeral V Unicode representation of Roman numeral Ⅴ, ⅴ prefixes penta-/pent- (from Greek) quinque-/quinqu-/quint- (from Latin) Binary 101 Octal 5 Duodecimal 5 Hexadecimal 5

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

The SI prefix for 10005 is peta (P), and for its reciprocal femto (f).

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## Evolution of the glyph

The evolution of our modern glyph for five cannot be neatly traced back to the Brahmin Indians quite the same way it can for 1 to 4. Later on the Kushana and Gupta Indians 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 look like a lowercase "h" mirrored and turned upside down. The Ghubar Arabs transformed the glyph in several different ways, coming up with glyphs that look more like 4s or 3s than 5s. It was from those characters that the Europeans finally came up with the modern 5, though from purely graphical evidence, it would be much easier to conclude that our modern 5 came from the Khmer.

In fonts with text figures, 5 usually has a descender, for example, Missing image
TextFigs256.png
Image:TextFigs256.png

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## In mathematics

Five is the third smallest prime number, after 2 and 3, and before 7. Because it can be written as 2^(2^1)+1, five is classified as a Fermat prime. 5 is the third Sophie Germain prime, the first safe prime, and the third Mersenne prime exponent. Five is the first Wilson prime and the third factorial 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. As a consequence of this, 5 is in base 10 a 1-automorphic number.

Five is a factor of 10, so vulgar 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.

The number 5 is a Fibonacci number, being 2 plus 3. The next Fibonacci number is 8. 5 is also a Pell number.

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.

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 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.)

## In various cultures

• There are five basic "pillars" of Islam.
• Muslims pray to Allah five times a day (Muhammad 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 norse mythology.
• 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.

## In music

• Using the Latin root, five musicians are called a quintet. One such group whose name celebrates their fiveness are the Jackson Five. (In an episode of Will & Grace guest-starring Janet Jackson, she declared that 5 is a mystical number and for that reason she must have precisely 5 backup dancers).
• The name of the band The Fifth Dimension implies that they are transcending beyond even the fourth dimension (time) into a new inner dimension.
• There was a British boy band called 5ive.
• Other bands with "five" in their name include We Five and the Five Stairsteps.
• The Dave Clark Five and the Ben Folds Five both named themselves after their lead singers, with an implied four others.
• The Vogues song "Five-o'clock World" came in reference to the hours 9 to 5 (ending at 5 p.m.), which are the hours of a standard work day. There are also five working days (non-week-ends) in a week.
• 5 is an album by Lenny Kravitz.
• "Take Five" is a famous jazz standard composed by Paul Desmond. It counts five beats per bar.

## In other fields

Five is:

• Art and Cultures
• Countries of the World (http://www.academickids.com/encyclopedia/index.php/Countries)
• Space and Astronomy