What 5 speed freewheels are compatible with a Sun Rims M13II rear wheel rim?
Freewheel thread sizes are standardized to an ISO standard which is 1.375" x 24 tpi. See https://www.sheldonbrown.com/freewheels.html. That means any new freewheel you can buy will be compatible with your new rear wheel.

The original Schwinn freewheel might have a different thread (I'm sure others will correct me on this if I'm wrong), but if you are replacing the wheels it's a good idea to replace the freehub too.