I wouldn't trust that with a modern CPU like what you have now... it might be alright at first, but you'd be getting really, really hot at load. That kind of heat kills processors fast.
If the processor is an i5-2500K, then it would probably be worth getting an aftermarket cooler. If the processor is only an i5-2500 with no K, then you probably won't be able to push it far enough to justify getting a heatsink to replace the one that came with it.
If you do in fact have an i5-2500k, the next step is to determine the physical size you can fit inside your case. A large 120mm tower cooler is going to work a lot better than a small 80mm top-down cooler, but is also going to take up a whole lot more space.