I have an 03 wrx
In 1st 2nd and 3rd gear it is working fine.
In 4th and 5th.,when I accelerate the engine revs -the tach goes up about a 1000 rpm,drops back and then starts to speed up.
It feels like the car is revving and then starts to speed up.
Is this a clutch problem?

 

Yup, your clutch is slipping...I see a new one in your future. I just replaced mine because it was slipping as well (50K miles). I replaced the clutch assembly, TOB and new updated flywheel (2002 had the clutch judder). You can either resurface your exisiting flywheel or put in a new lightweight one.