I wouldn't get a new processor. As the 5000+ is already a VERY good processor, this would be a waste of money. Unless your budget is vast, there is no point in replacing your CPU.
Since your case is the problem, I would first try buying a new case. Once you get the new case, you can check whether the motherboard you have will effectively fit into the new case. If it will, then you just have to rebuild the computer in the new case. If the motherboard will not fit, you will have to purchase a new motherboard, but no big deal. You will be able to reuse your ram, hard drives, dvd drives, etc.
If you must remove your heatsink from your processor, make sure to ask how to put it back on before you try!
Best of Luck