You want the good or bad news? On my table, NEC 430.248, a 7.5 HP single phase motor has a full load amp rating of 46 amps with a locked rotor amps rating of 480 amps ( the amount of current it draws when staring up) on table 430.251A. The circuit condutor must be 1.25% of the FLA or 57.5 amps which leaves you using #4. The circuit breaker must be 250% of the FLA which comes to 115 amps and since they don't make a 115 amp breaker, use a 125 amp breaker. That is if it's inverse time delay, if instantanous trip breaker, you'll have to go 800% of FLA or 368 amps!
Copper is getting expensive and you'll need 1" conduit. The main purpose of the circuit breaker is to provide short circuit protection, that's why you'll see high amp rating, this covers the inrush of amperage when the motor starts. The motor has it's own over load protection, again that's why you'll have such a high rating on the circuit breaker. The circuit breaker will work very fast on a short circuit!
I'm not a complete idiot, pieces are missing.