Assuming that D is a 5-(v,k,2) design, G is an automorphism group of D, and the socle of G,Soc(G)=PSL(2, 2n)， and by using the orbits of PSL(2,q)acting on the project lines, it is proven that G can not flag-transitively act on a non-trivial 5-(v,k,2) designs, which is a part rusult of the classification problem of flag-transitive t-designs.