I don't think the rpm you're at is the issue, but easy test of course is to leave it in 3rd or 4th instead of going up into 5th, to see if it feels the same at that speed. My guess, just a guess, is that the vibration is an issue at the rear of the car that you feel when accelerating and giving it gas b/c you're putting more weight on the rear in those situations.
I would expect that if the problem was with the engine or drivetrain, that it might go away when you put the clutch in, but not when you just let up on the gas while leaving it in gear.

edit: Unless of course the engine was missing, but I'm assuming you'd be able to tell that's what was happening.