Have lived here five years, occupying an apartment paying no rent

If he wants you out then yes, he can have you evicted. He would have to go through the same procedure as if he were evicting a tenant with a lease, including written notice for the required time and filing a lawsuit for eviction if you don't move out.

It would not be legal for him to just change the locks, though. Even though you don't have a lease and don't pay rent you are still considered a resident and he would have to follow the landlord/tenant procedure for that state.

If there's no written lease, then your "lease" is your state's landlord/tenant law (property code). If you're not in violation then he would have to give you the appropriate type of notice to terminate your rental agreement & have you move. (Typically 30 days notice - this can vary by state)

Eventually, he would be able to evict you by following the proper procedure - whatever it is in your state.