I have an old crankset from an 80s 10-speed (2x5) bicycle with downtube friction shifters. The chain currently in use is marked as "6/7/8 speed," but works fine on the 5-speed freewheel. For a multitude of reasons, one being the need for more gears, I have decided to replace the rear wheel and 5-speed freewheel with a freehub system and cassette sometime in the near future.
I know from riding the bike that the current 8 speed chain presents no problem to the front chainrings, but I would like to fit a 9 or 10 speed cassette onto the rear hub, which will necessitate a narrower chain. I would like to avoid having to replace the front crankset.*
I've read safety warnings online of using many-speed chains with few-speed chainrings, but given that my crankset was designed with a 2x5 system in mind (not 2x9 or 2x10), I'm especially worried about using a narrower chain.
Would a vintage 2x5 crankset be okay with a narrower 9- or even 10-speed chain? Or should I keep the 8-speed chain and "only" upgrade to an 8-speed cassette?
*Tangentially relevant: 9- or 10-speed square taper double cranksets don't seem to exist at all! Replacing my current 52/42 setup with a more modern 10-speed Hollowtech, or converting to a 1x system isn't out of the question, but I'd like to save as many of the original parts as possible while still keeping the bike usable by modern standards -- which means binning the old 14-26 freewheel.
EDIT: I want to thank @MaplePanda for explicitly wording my biggest concern in a comment:
For learning purposes: I’ve heard you run the risk of the chain getting wedged between the chainrings if you run a high speed count chain on a low speed count crankset. Is that an actual possibility? – MaplePanda
To be clear, this is precisely the safety issue I was referring to in my question above. I am not aware of any other potential issues with crank and chain compatibility, though I am of course open to learn.