It is one of the natural number lies between 4 and 6.
How “5” is used in Mathematics?
In the prime number series 5 stands in the 3rd position (1, 3, 5, 7…).
5 can be written as 221+1, so it is classified as a Fermat prime.
5 serve as
: The 3rd Germain prime
: The 1st safe prime
: The 3rd Mersenne prime exponent
: The 3rd factorial prime
&
: The 3rd Catalan number
Five is the first known good prime which is an Eisenstein prime number that neither have imaginary part nor it have real part. Eisenstein prime takes the form 3n − 1.
5 is the 5th number in the Fibonacci series (1,1,2,3,5,8…).5 appears in all the Markov Diophantine equation: (1, 2, 5), (1, 5, 13), (2, 5, 29), (5, 13, 194), (5, 29, 433), … so it is also serves as the Markov number.
In numbers whose base is 10 or 20, 5 serves as a 1-automorphic number.
Normally in mathematics polynomial equations of degree 4 and the below like 3, 2 can be easily solved with radicals. But the degree of equation is 5 and above those can’t be solved.
This is called as the Abel–Ruffini theorem. It is due to the fact, that the symmetric group Sn is solvable if the group is in the order n ≤ 4 and it is not solvable if n ≥ 5.
A graph which is having four or fewer vertices is usually a planar but there some kind of graphs exists with 5 vertices those are usually not planar: K5, the complete graph with 5 vertices.
Generally a planar graph is a graph which can be drawn on the plane. In these graph edges of the vertices intersect only at their endpoints. Other way around, it can be said edges of vertices will not cross each other.
If a polygon is made up of five sides then it is called as pentagon.
A polygon with five sides is a pentagon. Polygonal numbers representing pentagons which also called as the pentagonal numbers.
Another one fact about 5 is the only prime number that ends with the digit 5. It is because all other numbers written with 5 in their one’s place are multiples of 5. So normally the 5 in base 10, five is called as 1- automorphic number.
called as 1- automorphic number.
Table of Elementary operations
Multiplication
| Multiplication | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | … | 1000 |
| 5* X | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | … | 5000 |
Division
| Division | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | … | 15 |
| 5/ X | 5 | 2.5 | 1.66 | 1.25 | 1 | 0.833 |  |
0.625 |  |
0.5 | .. |  |
| x/5 | 0.2 | 0.4 | 0.6 | 0.8 | 1 | 1.2 | 1.4 | 1.6 | 1.8 | 2 | 3 |
Exponentiation
| Division | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 5x | 5 | 25 | 125 | 652 | 3125 | 15625 | 78125 | 390625 | 1953125 | 9765625 |
| X5 | 1 | 32 | 243 | 1024 | 3125 | 7776 | 16807 | 32768 | 59049 | 100000 |
Glyph evaluation history
The evolution history of the current modern glyph of five cannot be traced back to the Brahmin Indians such that we have done for the numbers 1 to 4. Indian Empires of Gupta and Kushana had many different glyphs. Interestingly they had no similarity with our modern glyph of 5.
The empires of Punjabi and Nagari have taken these glyphs those are similar to the lowercase letter “h” rotated to 180°. Later on The Ghubar Arabs has transformed the glyph in many different ways just as Gupta empires. This time more or less it was similar to 4 or 3 than the number 5. From these character representations Europeans finally have given the shape of modern 5.
How five is represented in various languages and numbering systems
| Cardinal | 5 five |
| Ordinal | 5th fifth |
| Numeral system | quinary |
| Factorization | prime |
| Divisors | 1, 5 |
| Roman numeral | V |
| Roman numeral (Unicode) | Ⅴ, ⅴ |
| Greek | ε (or Ε) |
| Arabic | ٥,5 |
| Arabic (Persian,Urdu) | ۵ |
| Ge’ez | ፭ |
| Bengali | ৫ |
| Punjabi | ੫ |
| Chinese numeral | 五，伍 |
| Devanāgarī | ५ |
| Hebrew | ה (Hey) |
| Khmer | ៥ |
| Telugu | ౫ |
| Malayalam | ൫ |
| Tamil | ௫ |
| Thai | ๕ |
| prefixes | penta-/pent- (fromGreek)quinque-/quinqu-/quint-(from Latin) |
| Binary | 101 |
| Octal | 5 |
| Duodecimal | 5 |
| Hexadecimal | 5 |