Persona 5 is everything I was hoping for and more. I'm incredibly grateful it ended up coming out for PS3, otherwise I would have missed this gem. The PS3 version looks great and runs well. The only issue I ran into was that load times were pretty bad and relatively common. So if you can deal with that, you're good.
Without spoiling anything, I will say I didn't care as much for the plot of characters as I did Persona 4. This game is quite a bit darker than Persona 4. Which is weird to say considering P4 basically started with a corpse. But there was always an air of hope to it to me, even when things got bad. Persona 5 starts off by telling you how screwed you are, and from there things get worse. Even basic things like the velvet room convey an air of hopelessness. It does lighten up, but expect some pretty rough stuff in the first section of the game.
As is with all the Persona games I've played, one of the big draws is your social links. Many of the characters are interesting and well-written. And the payoffs for those you truly come close to is excellent. There were a couple I wasn't a huge fan of, but none of that felt as wasted as, say, the mother or student from Persona 4. There's also the bonus that all social links assist you in some way, not just powering up your fusions.
As for the gameplay, this is easily the best for me. Non-randomized dungeons feels a lot better. They've brought in the negotiations from the SMT series as well, for better or worse. As a note that may help, there is a tutorial on how to better negotiate with demons. The only gameplay complaint I have is that they really spread the damage types too thinly. You have ten different damage types now. But beyond the core four elements, the weaknesses drop off quite a bit.
The biggest thing I love about this game, and indeed this series, is the style it has. It's visually unique. Every screen and menu is oozing with style, standing out compared to most other games. It's really cool in my opinion.
If you're a fan of Persona, SMT, JRPGs in general (there are shades of Pokémon here), or visual novels, I'd recommend checking it out. If you have a PS3, this version is cheaper and only really sacrifices load times as far as I can tell.