If you look around, you can find a SunTour New Winner "Ultra 6" freewheel that fit in 120 mm OLD, replacing a 5-speed freewheel. They also made a (perhaps more available because more popular in the day) "Ultra 7" that was 7 speeds fitting in 126 mm OLD. I have one of those, along with a SunTour regular New Winner 6 for 126. All 3 of these shift fine with a 3/32" chain, but I think that their smallest cog may be 13 or even 14, and they are not "Hyperglide" type with teeth machined to facilitate chain transfer -- instead they shift with more of a "clunk" (which I find very satisfying, but it's not modern). More recently Shimano, SunRace and SunLite have made 7-speed freewheels (13 or 14 to 28), but whether those fit on 126 mm or require 130, I'm not sure.
Those seem to be more "Hyperglide" types.
Another option,
if your 10-speed wheel is Shimano--freehub-compatible (includes SRAM, SunRace, IRD for the most part) and you don't mind re-dishing it somewhat, is to fit an earlier model of the Shimano Hyperglide (or Hyperglide/Uniglide compatible, same function) freehub that was intended for 7-speed cassettes. It's about 3 mm shorter than the one for 130 and 135 mm OLD 8-speed cassettes -- you might be able to get a wheel configured with that down below 130 mm OLD, and you could even use Sheldon Brown's "
8 of 9 on 7" or "9 of 10 on 7" method to achieve some More Cowbell in that department. (Go to that link and search for "8 of 9 on 7"; but I advise you to
read the whole page, which is incredibly informative.) An advantage of going this way would be that you'd be more likely to have the friction shifting work with older shifters -- less total cable travel required -- and yet give you way more than 5 speeds rear.