Likely the original capacitors on the motor are bad, since you were able to help it start. You might consider taking the motor to a shop to have them check it out. Or you could just wire in the new capacitors you have and see if that works.
I don't think the larger wire is going to help. 10 Ga is recommended for a 5 HP motor, but 12 Ga will work, it'll just get a bit warmer.
