Hopping back and forth between PS4 and PS5?

Hi all,
We have a PS4 and a PS5. I play on my PS5 and my son has shown an interest in it. If I buy him a copy for the PS4, can he hop between his account on the PS4 and his account on the PS5? We have seen some games (CoD I believe was one of these) where he bought the ps4/ps5 combo, started on the ps4, played the upgrade version on the ps5 but when he went to back tp the ps4 to play, it wouldn't let him. I am trying to avoid the same thing here.
He has a SQ ID and all. I would like to play with him but and don't want to end up where he hops onto the ps4 and it won't let him play after he logs into the ps5 with his account. Thanks all for the help in advance. :)

I jump between my PS5 and my PS4 several times a week, works without any issues :)

Thanks a lot! I appreciate the quick reply too!!!! :) LOL He asked me how long it would take to hear a reply back and this was super quick. Thanks again :)