A stronger spring will cause the engine to rev higher but will defeat the purpose of the governor. Is the cable adjusted so the lever reaches full throttle?

The throttles don't open very far at full speed, just like your car. They respond to sudden needs for gas by opening further, but return to a near-closed position.

Yes, the governor is adjusted so that when the engine is off the governor arm pushes the throttle all the way open. I guess I was thinking that with only 5hp to work with the engine should be running at say 3/4 throttle with the additional 1/4 throttle left for extra heavy load (snow).

I doubt that the throttle is even 1/4 open when at fast speed. You'll need a manual to adjust the governor. You loosen the governor arm screw and move the arm's shaft and re-tighten again Sometimes the arm's shaft is fully clockwise at full throttle or full counterclockwise. You can experiment. Also, is the governor linkage in the correct hole? The throttle must be wide open for the test.