It is most easily described as graph of a pentagram embedded inside a pentagon, with a total of 5 crossings, a girth of 5, and a Thue number of 5. The Petersen graph, which is also a distance-regular graph, is one of only 5 known connected vertex-transitive graphs with no Hamiltonian cycles. The automorphism group of the Petersen graph is the symmetric group 
  
    
      
        
          
            S
          
          
            5
          
        
      
    
    {\displaystyle \mathrm {S} _{5}}
   of order 120 = 5!. The chromatic number of the plane is at least five, depending on the choice of set-theoretical axioms: the minimum number of colors required to color the plane such that no pair of points at a distance of 1 has the same color.
Under the FIBA rules, A player fouls out and must leave the game after committing five fouls
Five-a-side football is a variation of association football in which each team fields five players. In ice hockey:
A major penalty lasts five minutes. There are five different ways that a player can score a goal (teams at even strength, team on the power play, team playing shorthanded, penalty shot, and empty net). The area between the goaltenders legs is known as the five-hole. In most rugby league competitions, the starting left wing wears this number. An exception is the Super League, which uses static squad numbering. In rugby union:
A try is worth 5 points. One of the two starting lock forwards wears number 5, and usually jumps at number 4 in the line-out. In the French variation of the bonus points system, a bonus point in the league standings is awarded to a team that loses by 5 or fewer points. Technology
5 is the most common number of gears for automobiles with manual transmission. In radio communication, the term "Five by five" is used to indicate perfect signal strength and clarity. On almost all devices with a numeric keypad such as telephones, computers, etc., the 5 key has a raised dot or raised bar to make dialing easier. Persons who are blind or have low vision find it useful to be able to feel the keys of a telephone.