Opsut showed that,for any graph G,the competition number of G is less than or equal to the edge clique cover number of G in 1982.This paper constructs the edge clique cover of minimum size and give the edge clique cover number for the complete pentapartite graphs K_n,n,n,n,n where n≡1,5(mod6).Then the new bound for the competition number of Kn,n,n,n,n is given by the relation of the edge clique cover and the competition graph,which improve the result of Opsut on the bound for the competition number of Kn,n,n,n,n.