5 month old puppy has one eye closed?

I think you did the right thing first which was to get a damp cloth and wash it. He might have something in his eye that's irritating it. If he will let you, try to open it slowly while using the warm cloth and if you can get it open then sweep the eye itself a couple times with the cloth. It might help remove dirt or whatever may be in there. If he keeps it closed or it starts to swell and have discharge, it would be time to go to the vet.