ahhhhh. haven't played 5 yet, but i would have thought they'd keep that feature.Reminisce doesn't do that anymore. It's for watching cutscenes you've unlocked in 5 now. They've likely gotten rid of it because of the immense size it would take to keep up with everything from 1-4.
Your best bet is to just start it. There's definitely callbacks to characters that fans from the start get more out of, but they're not necessary as everything is a contained story anyways.
of course the real solution here is to play 4 before 5, right?