We show that, if NP language L has an invulnerable generator and if L has an honest verifier standard statistical ZKIP, then L has a 5 move statistical ZKIP. Our class of languages involves random self reducible languages because they have standard perfect ZKIPs. We show another class of languages (class K) which have standard perfect ZKIPs. Blum numbers and a set of graphs with odd automorphism belong to this class. Therefore, languages in class K have 5 move statistical ZKIPs if they have invulnerable generators.