The converter youre thinking of is actually called a transformer and buck boost transformers are the specific type usually used for motors in this situation. For your specific situation you would need a transformer with a 2:1 ratio(120v primary, 240v secondary). Using the ratings on your motor's nameplate which says 15a(which is about half of what is listed in the NEC FLC chart for a 5hp motor; this is probably because most manufacturers grossly over rate their motors), u would need a 5-6kva transformer. This size includes approxamately 25% extra capacity which is needed for motor starting 'in-rush' currents. In general, transformers should be slightly oversized for the load to prevent saturation of the core.
Keep in mind that when voltage halves, current doubles, and thus the transformer will draw double the current of the secondary, on the primary 120v side. In your case, this would be approx 30a of 120v power while the motor is running. And during starting, the in rush current can be 6-8x as much. Which also needs to be factored into the circuit(such as the size of the breaker).
Taking all this into account, one big question comes to mind:
Is your 120v source circuit large enough to handle the above calcs? Probably not! In which case i would run a new circuit for the compressor!
And having said all this, transformers aren't cheap, and factoring in the required breakers/disconnects, wire, etc, for a separately derived system, it would be cheaper to either wire in the proper 240v circuit, or get a smaller 120v rated motor!
