It sounds like the synchros aren't fully disengaging when you put it into 5th. Synchros, combined with the clutch pedal, are what allow you to shift a manual transmission. In theory, they don't line up properly until you either "hit the sweet spot RPM-wise" or engage the clutch. Try this simple experiment:
From a dead stop, place the transmission in 1st and start off normally. When the point where you normally shift into 2nd arrives, shift into either 3rd or 4th. If the clutch is working properly, the car should buck quite a bit and the engine may die. If not, if the engine only lugs a little and the car keeps going, the clutch needs to be loosened. However, since you didn't say you're having a similar problem in any other gear, I'd say it's the synchros.
Try finding a transmission in a junkyard, or rebuild the one you have.
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Saturday, June 18th, 2011 AT 7:54 AM