OK, From the BTDT section I can tell that a "5 Horsepower" compressor motor is really "5 Whorespower".
Secondly, you don't really need a 3400 RPM motor.
Get yourself an 1740 RPM 3 Horsepower motor, and use a bigger pulley on it.
You will be many miles ahead!
I had the same "5 Horsepower" motor on a compressor, you could cook eggs on it, it was wasting SO much power. Most of the electricity it used was wasted heating the air in the shop. I got a three horse motor, 1740 RPM and got about an 8" pulley for it. The compressor runs a little bit slower, but MUCH cooler. And the I burned out the first compressor head, the second one is running cool and strong for years at the very slightly reduced speed.
The 3 HSP motor runs cool to the touch. So I KNOW it is not wasting all the expensive electricity turning it into wasted heat.
You could go up to about a 10" pulley on the motor, and get to the original speed of the compressor, but I would recommend a little bit slower, and longer.
Measure the original diameter of the pulley for the calculations.