A few hours later he replied "hmm, well, I prefer the original software and I can't get that running, but according to the box [of the scanner] it should work with Windows XP."
So in the end my dad managed to find an old XP computer from 2005 somewhere in his attic, set it up (without internet of course) just to scan his old negatives and slides, then does all the actual editing work on his new laptop. It works but the old computer is clearly the bottleneck.
I think the next time I visit him I'll try to get the software running with Vuescan instead, it probably would be faster (the scanning software always uses 100% of the CPU while scanning, so that might actually be more of a bottleneck than the USB2.0 connection). Plus I wouldn't mind supporting the developers behind it.
(also, re:"get a new scanner", I'm not sure how slide scanners these days would compare to that 5400. Sometimes technology peaks and then gets worse, especially on the consumer end as the market shrinks, and I wouldn't be surprised if this is true for film scanning tech)