I'm in the process of fixing up an old Suteki mixte and I am unable to use the original wheels since the spokes are rusted out. I plan on rebuilding them at some point, but can't spend the money on spokes right now.
I have a wheelset that I took from another bike that i think should work except for one thing, the Suteki is a 10-speed and the borrowed wheelset came from a 12-speed. I could swap the freewheels, but will that cause some spacing issues? What would be the best solution? Can I just add a spacer to make up for the sixth cog or am I going to have to re-dish the wheel?

My guess is you won't need to do anything more than adjust the rear derailleur limit screws. Give it a try.

+1. Going between 5 and 6 cogs in the back shouldn't be an issue.

Great! I'll give a try and report back. Thanks!

Measure the frame once you take the wheel out, 6 speed needed another 6mm, width.
over the 120 needed for 5, But you can probably wrestle it in ..

I just measured it, and the spacing is 126mm.

It will fit, It's just a little tighter getting it in.

Well the rear derailleur didn't even need to be adjusted! I still need to fiddle with the front derailleur a little, but the whole process was surprisingly easy. Thanks for your help guys.