Yes, there is a statute of limitations.
No, your husband cannot file charges. All he can do is report the matter to the cops or the local prosecuting attorney. It will be up to the cops whether it's worth investigating, and it will be up to the prosecutor to file charges or not.
I don't know what the SOL is in SC, but, after 5 years, and given the divorce context, I seriously doubt anyone will put much stock in your husband telling tales.