Persona 5 is definitely a good game that I think you'll enjoy. I got it last week and needless to say, I love it. Many others love it. And so I think you'll love it.
Little Big Planet(More specifically for the PS4, Little Big Planet 3), is another amazing PlayStation exclusive. It's sort of like ROBLOX in a sense that you build maps, movies, and all that, and then share it with others across the world. You even have your own little character("Sackboy" or "Sackgirl"), that you can customize. If you get a PS4, then you can get Little Big Planet 3, which as of now, can essentially be considered the last Little Big Planet game. The game Dreams, was made by the same people who created the original Little Big Planet, the PSVita version, and the second installment too(Media Molecule). I think Dreams has the same concept and design as Little Big Planet, although I believe it's more advanced, thanks to modern hardware and software nowadays.
Infamous, is another series that is exclusive to PlayStation. The latest one was Infamous: Second Son, which was released back in 2014, followed by a spin-off game a few months after launch. The original Infamous and Infamous 2, is unfortunately only available on the PS3 though. But either way, I enjoyed Second Son, and so perhaps you'll enjoy it.
Well, these are all of the recommendations I could give you based on what I've played. Most games that I have played, are supported on multiple platforms, rather than being exclusive to PlayStation. If you'd like any other recommendations, then perhaps telling us what specific genres you like(Survival, RPGs/JRPGs, FPS etc.)