I have 2 X 125mm Wheels and I am looking for a ~5,000 rpm motor to connect to it. Do you have recommendations?
I want to build a shuttle-feeding machine to play badminton.

 

How would a sewing machine motor go?
A second hand sewing machine would be easy to get and it comes with a speed control too.

 

The simple sewing machine motor is a series universal motor and the speed varies with the load, So the TS will need to have a fairly heavy flywheel.