Loss of power in 3-5 gears
 

I recently purchased an 87 Honda CRX HF. The car runs great in 1st and 2nd gear and the engine will turn 6,500 rpm. When I shift into 3rd, 4th, and 5th gears and try to accelerate hard the engine will bog down. If I back off and accelerate slowly the car will slowly start to accelerate and I can finally get to 70 mph. The car has no power going up steep hill and I have to down shaft to 2nd gear and 30 mph to get up the hill. Any ideas what is wrong?

Your clutch is slipping if the rpm go up but the mph do not.

The clutch is not slipping. The mph goes up as the engine goes up. The engine rpms will not go up under hard acceleration in 3rd-5th gears, it acts like it is starving for gas but the car does not have the problem in 1st and 2nd gear.

possibly vacuum leak

If the system is PGM-FI, then check for a trouble code:

Attachment 13615