I don't know if it is still true but when I was younger IC motors were universally over rated about double. A five hp gas was equivalent to a 2 1/2 hp electric.
I have heard this as well, never seen it defined anywhere though. Regardless, to determine if you could use a smaller HP motor, or what the HP needs to be, you should look at the pump rating in CFM and pressure at a rated rpm input and determine your needs. A bit of a way to cheat would be to just compare those specs to other compressors and see what HP they run, but as noted previously be wary of HP ratings tied to the motors that list the duty rating as “spl” or “special”….those are the inflated HP motors. Watch the amps, that will tell the story.
Also someone mentioned using a 2 pole motor and “gearing it down”, which would mean dropping the size of the pulley, typically to 1/2 the diameter of an equivalent 4 pole motor. Since the compressor pulley is a fixed diameter (it’s integral to the pump serving as a flywheel and cooling fan) you can only adjust the motor pulley. Dropping the diameter in half may start to put you in the realm of not having enough diameter, which translates to length of belt in contact with the pulley groove, to transmit the HP. Again, there are tables and information available on the web.
What CFM and pressure is the pump?