5 (number)

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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)

0 1 2 3 4 5 6 7 8 9 >> List of numbers -- Integers 0 10 20 30 40 50 60 70 80 90 >>
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
Vigesimal	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).

Contents 1 In mathematics 1.1 In numbering systems 2 The Arabic glyph 3 In science 3.1 In astronomy 4 In various cultures 5 In music 6 In sports 7 In technology 8 In other fields 9 Years

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. It is an Eisenstein prime with no imaginary part and real part of the form <math>3n - 1</math>.

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 and a Markov number, appearing in solutions to the Markov Diophantine equation: (1, 2, 5), (1, 5, 13), (2, 5, 29), (5, 13, 194), (5, 29, 433), ... (A030452 lists Markov numbers that appear in solutions where one of the other two terms is 5).

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 decimal, duodecimal and vigesimal) five is 5.
• The Roman numeral for five is V, which comes from a representation of an outstretched hand.
• In the Greek alphabet, ε (epsilon) has numerical value of 5.
• In the Hebrew alphabet, ה (heh) has numerical value of 5.
• In the Cyrillic alphabet, Е has numerical value of 5.
• In the Glagolitic alphabet, Image:GlagolitsaDobro.gif (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).

The Arabic glyph

Image:Evolution5glyph.png

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" rotated 180°. 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, Image:TextFigs256.png.

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 NGC 5, a magnitude 13 spiral galaxy in the constellation Andromeda
• The Saros number 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 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.
• 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 East Asian 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 via the identification of the elements with the five planets visible with the naked eye.
• In some cultures there are five cardinal directions, including the center.
• 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.
• According to eastern mysticism human beings are made of five elements water, earth, air, fire and aether (also called "ether"). These five elements are also referred to as "Pancha Tatva".

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, Five Stairsteps and the Five Man Electrical Band.
• 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.
• Jurassic 5 is a hip hop group whose second full length album was titled "Power In Numbers."

In sports

• The number of players on a basketball team.
• In chess, the number of first titled grandmasters.
• In chess, the fewest number of moves a pawn makes to a queening square.
• 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).
• The number of kyu (pupil) grades in judo
• 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 technology

• The Pentium, coined by Intel Corporation, is a fifth-generation x86 architecture microprocessor.
• On most phones, the 5 key is associated with the letters J, K, and L, but on the BlackBerry it is the key for G and H.

In other fields

see also 5 (disambiguation)

Five is:

• The number of oceans in the world.
• The five senses are sight, smell, hearing, touch and taste.
• The five basic tastes are sweet, salty, sour, bitter and umami.
• Pentameter is verse with five repeating feet per line; iambic pentameter was the most popular form in Shakespeare.
• In the United States legal system, the Fifth Amendment to the United States Constitution can be referred to in court as "pleading the fifth", absolving the defendant from self-incrimination
• The note in the English monetary system that features Elizabeth Fry. (£5 Note)
• The denomination of the U.S. dollar with Abraham Lincoln's portrait.
• The number of cents in a nickel. The U.S. nickel bears a portrait of Thomas Jefferson. The Canadian nickel has a beaver on its reverse.
• The designation of an Interstate Highway that runs from San Diego, California to Blaine, Washington.
• 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.
• Five babies born at one time are quintuplets. The most famous set of quintuplets were the Dionne Quintuplets born in the 1930s.
• In Astrology, Leo is the 5th astrological sign of the Zodiac.
• 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 The Fifth Element.
• The number of dots in a quincunx.
• The number of points in a pentagram.
• The Garden of Cyrus 1658 by Sir Thomas Browne is a Pythagorean Discourse based upon the number 5.
• 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.
• The holy number of Discordianism, as dictated by the Law of Fives.

Years

• Historical years: 5 A.D., 5 B.C., or 1905