Your graphics card should be fine as it's roughly equivalent to a GTX560.

The FX6300 is cheap for a reason. It's roughly equivalent to an i5-760 (3 generations old) and not something I would recommend to anyone.

If your budget for CPU is $110, you won't even get a good 5-boxing CPU for that. And the motherboard it uses is LGA775, which would need to be upgraded as well to support current i5/i7 CPUs (or even the current AMD CPUs that are fast enough to 5-box with), so that's another $150. Then you'd have to upgrade the memory too, which is another $115-150. Power supply might be OK depending on how old it is.

What's your budget?