The sequel should be cross gen. Its what they could have done for God of War 2, and should do for 5 as that would make its initial sales huge and make its legs big as next gen consoles catch up in userbase and that way it will also take advantage of next gen hardware.
I'm 99% sure PS5 will be backwards compatible with PS4. BC will be a very important feature next gen to keep players within the ecosystem. Most of us these days have a digital library that we can't sell off or give to a kid in the family like we used to in the past and I'm sure Sony and MS know this. With PS4 having such a huge pie of the marketshare Sony would have to be mentally challenged to not capitalize on it by letting PS4 players carry over their library into next gen. MS has already made it clear that they will keep BC from here on out. In light of that I think this whole cross-gen business makes no sense. God of War sequel will likely release a year after Horizon Zero Dawn sequel (which I expect to be a launch title) and at that point I think Sony will be looking to drive PS5 sales and not PS4.