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Let G be a finite group, and S a subset of G1 with S=S-1. We use X=Cay(G,S) to denote the Cayley graph of G with respect to S. We call S a CI-subset of G, if for any isomorphism Cay(G,S)Cay(G,T) there is an α∈Aut(G) such that Sα=T. Assume that m is a positive integer. G is called an m-CI-group if every subset S of G with S=S-1 and |S|≤m is CI. In this paper we prove that the alternating group A5 is a 4-CI-group, which was a conjecture posed by Li and Praeger.