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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- (Greek) quinque- (Latin)
Binary	101
Octal	5
Duodecimal	5
Hexadecimal	5

5 (five) is the natural number following 4 and preceding 6. Prefixes for 5 include penta- (Greek) and quinque- / quint- (Latin).

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

Contents

1 Evolution of the glyph 2 In mathematics 2.1 In numbering systems 3 In science 3.1 In astronomy 4 In various cultures 5 In music 6 In other fields

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 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 Mersenne prime exponent. Five is the second Wilson 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 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 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.

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 numbering systems

• In binary code five is 101
• In ternary code five is 12
• In quaternary numeral system code five is 11
• In quinary five is 10; in senary code and all codes above (such as octal, decimal and hexadecimal) five is 5.
• The Roman numeral for five is V, which comes from a representation of an outstretched hand.
• In Greek alphabet, ε (epsilon) has numerical value of 5.
• In Cyrillic alphabet, Е has numerical value of 5.
• In Glagolitic alphabet, (dobro) has numerical value of 5.
• The kanji and Chinese character for five are both 五, and its formal writing in Chinese is 伍 (pinyin wǔ).

In science

• The number of appendages on most starfish, which exhibit pentamerism.
• Almost all amphibians, reptiles, birds and mammals which have fingers or toes have five of them on each extremity.
• The maximum category on the Saffir-Simpson Hurricane Scale, the most damaging.
• The atomic number of boron.

In astronomy

• Messier object M5, a magnitude 7.0 globular cluster in the constellation Serpens.
• The New General Catalogue object http://www.ngcic.org/ NGC 5 , a magnitude 13 spiral galaxy in the constellation Andromeda
• The Saros number http://sunearth.gsfc.nasa.gov/eclipse/SEsaros/SEsaros1-175.html of the solar eclipse series which began on April 4, 2720 BC and ended on May 24, 1422 BC. The duration of Saros series 5 was 1298.1 years, and it contained 73 solar eclipses.
• The Saros number http://sunearth.gsfc.nasa.gov/eclipse/LEsaros/LEsaros1-175.html of the lunar eclipse series which began on -2581 October 8 and ended on -1084 March 24. The duration of Saros series 5 was 1496.5 years, and it contained 84 lunar eclipses.

In various cultures

• There are five basic "pillars" of Islam.
• Muslim 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.

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.

In other fields

Five is:

• The expression "five by five" originates from the U.S. Military and refers to the five levels of signal strength and signal clarity in a radio transmission. The fifth, and highest level for each being, "Loud" and "Clear" respectively. Thus "five by five" was adapted to define anything ideal.
• The number of oceans in the world.
• The number of cents in a nickel, a coin with Thomas Jefferson's portrait.
• The denomination of the U.S. dollar with Abraham Lincoln's portrait.
• The designation of an Interstate Highway that runs from San Diego, California to Blaine, Washington.
• The number of players on a basketball team.
• The number of permanent members with veto power on the UN Security Council.
• The number necessary to make a majority decision in the U.S. Supreme Court.
• The five senses are sight, smell, hearing, touch and taste.
• The five basic tastes are sweet, salty, sour, bitter and umami.
• Five babies born at one time are quintuplets. The most famous set of quintuplets were the Dionne Quintuplets born in the 1930s.
• The word "quintessential" came from that elusive fifth element that completes the basic four elements (water, fire, air and earth). There is also a movie called Fifth Element.
• The number of dots in a quincunx.
• The number of points in a pentagram.
• Pentameter is verse with five repeating feet per line; iambic pentameter was the most popular form in Shakespeare.
• The expression "five-finger discount" refers to shoplifting.
• The five stages of grief are said to be shock, denial, anger, bargaining and acceptance.
• The Garden of Cyrus 1658 by Sir Thomas Browne is a Pythagorean Discourse based upon the number 5.
• Giving five refers to slapping hands with someone as a sign of approbation.
• The word "punch" comes from the Hindustani for five. Being true to the designation of punch, the drink Five Alive is named for its five ingredients.
• Something that tries to bring an operation down or screw with the system can be called a "fifth wheel".
• Aside from Hawaiian punch , the 50th state of the United States gives us the quinary TV show title Hawaii Five-O.
• The Olympics have five interlocked rings as their symbol, representing the number of inhabited continents represented by the Olympians (counting North America and South America as one continent).
• In chess, the number of first titled grandmasters.
• In chess, the fewest number of moves a pawn makes to a queening square.
• The number of kyu (pupil) grades in judo
• Five Tiger Generals
• Five-spice powder
• Five Principles of Peaceful Coexistence
• Five Dynasties and Ten Kingdoms Period
• Five the UK TV channel.
• In rugby union, the number of the lock forward who usually jumps at number 4 in the line-out.
• In baseball, five represents the third baseman's position.
• In the DOS Shell and Windows, the F5 key refreshes a directory listing or folder window. In Internet Explorer, the F5 key refreshes the current webpage.
• The Pentium, coined by Intel Corporation, is a fifth-generation x86 architecture microprocessor.
• 5, a character in the comic strip Peanuts
• Historical years: 5 A.D., 5 B.C., or 1905
• Enid Blyton's The Famous Five
• The automobile Renault 5
• The juice brand 5 Alive
• To 'hang five' in surfing is to surf with one foot partly off the board.