I have an old five speed cassette from a Schwinn Touring bike, on an ancient single wall rim that is failing. I was curious if I could thread said cassette onto a Velocity Deep V rim w/ a flip flop Formula hub?
To be picky, that's probably an freewheel and not a cassette you're talking about.
But yes, it would fit the freewheel side of a flip flop hub.
Do note that the FF hub might be set up for another dropout spacing, and might not have the axle length required to take a 5 speed freewheel.
And if you get past that hurdle, odds are that the dish of the wheel will be off.
I am pretty sure you can't adjust the axle spacing in the normal manner on those formula flip-flop hubs (the ones with sealed bearings and shouldered axles) so you might not even be able to get to the re-dishing stage. In it's stock configuration I doubt there would be room to cram a 5 speed freewheel on there. It should thread right on but will probably stick out too far and rub on the frame.
The flip/flop wheel is already 120mm wide. The hub would wind up too wide. You could stretch the frame apart in order to accomodate it but then the rim would be off-center.
You can fix the rim but only if you are good with a spoke wrench.
My flip flop wheel does not have any spacers between cone nut and locknut; it's simply a wider wheel. It's not a Velocity but unless someone here has done it, we shouldn't assume you can just convert it into a 5 speed wheel with a few tweaks.
Why not use the flip flop wheel with a single freewheel? Lots of folks like singlespeeds, and your legs will get stronger.
Or, if you haven't bought anything yet, go to niagaracycle or bikepartsusa and buy a 5-6 speed freewheel rear wheel. there's steel (cheaper) and aluminum (higher) but they're both less than a flip flop. The 5/6 is the correct one because there was a 6 speed ultra narrow before they went to 126mm wide regular 6 speed. If you want a higher end wheel, I think Harriscyclery.net has them.