I stripped the fixed side of my formula hub last year, and the nice rebuilt wheel is sitting uselessly in my front room. I got the idea of turning my current fixed bike into a road bike with a few bits I had laying around, and using the free side of the formula hub for a 5sp freewheel. Does this work? I only know about 1sp freewheels, and I've never had a freewheel bike with a thread on fw.

Yeah it should. But you have to dish the wheel.

it should. maybe.
at minimum you'll have to respace the axle. actually get a new axle in the first place - the one IRO uses for the 130mm spacing *might* be long enough.
then dish the wheel

the small problem with respacing your axle to allow room for a multispeed freewheel is that the bearings are sealed, and the axle cannot be moved from side to side to allow for more spacing on one side than the other. So, if you can add enough space on one side to clear the five speed, and still have enough room to put a nut on (and can stretch the frame to the new spacing), then you are all set - don't bother with the fact that one side is longer than the other.

I was hoping that it would just be a case of redishing - the frame I would be using is was a ten speed once upon a time. If I have a 120 hub and a 120 spaced frame, would I have to move the axle?

Maybe it should just be a singlespeed after all. Or I should keep my eyes peeled for a set of wheels.

The 5-spd freewheel will stick out past the end of the 120mm hub. That's why you need the axle spacers, to push out the cone locknuts or whatever so the inside of the dropouts doesn't push up against the freewheel itself. When you do that, the spacing will probably be in the 130mm range, possibly higher.

Might be doable, but a 1-spd freewheel would be a lot less trouble. And you wouldn't have to worry about ders and shifters.