Sony announced today that Playstation 5 will be backwards compatible with all but 11 games from the previous generation. Meaning all PS4 Yakuza titles, including Judgment, Ishin!, and Fist of the North Star, will be available to play on PS5 at launch! On top of that PS5 owners can expect extra performance from most titles on the Playstation 5 (for select titles). This includes things like better framerate, faster loading speeds, and higher resolution.
Backward compatibility: PS4 games playable on PS5 consoles
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Yakuza 4 Coming Exclusively to PS3 in Spring 2011 – PlayStation.Blog