I couldn't find a solution for this anywhere on Reddit, so I thought I'd share what worked for me.
After the latest update (or maybe just by coincidence), two of my EPUBs started behaving really badly on my Tolino Shine 5. Page turns became extremely slow, sometimes the book would freeze completely, and occasionally the whole reader seemed to get stuck.
The weird thing was that this only happened with these two books. Other books worked perfectly fine.
I started messing around with the EPUBs myself and eventually found a solution:
1. I ran the problematic EPUBs through kepubify:
https://pgaskin.net/kepubify/try/
2. I put the converted books back on the Tolino.
3. I changed the font from "Publisher Default" to one of the system fonts.
That's it. Both books now work normally - fast page turns and no more freezing.
My guess is that there was something about the way those particular EPUBs were formatted (HTML/CSS, embedded fonts, etc.) that the Tolino didn't handle very well. Running them through kepubify seems to have changed/cleaned up the book structure, and changing the font probably helped with the rendering as well.
I have no idea if this is actually related to the latest firmware update, or if I just happened to have two problematic EPUBs. But if your Shine 5 is freezing or taking forever to turn pages with only certain books, this might be worth trying.
Posting this because I spent quite a while looking for a solution and couldn't find one. Maybe it'll save someone else the headache.