Let G be a finite group and ω(G) be the set of element orders of G. Let k ∈ ω(G) and s k be the number of elements of order k in G. Let also nse(G) = {s k | k ∈ ω(G)}. In this thesis we prove that if G is a group such that nse(G) = nse(L 5 (2)), then G ∼ = L 5 (2). this thesis has been written based on [21].