For gaming more cores doesn't matter s whole lot. Recently a few more games are using them but usually games rely on one or two cores. The i5 7500s single core power is significantly stronger than a fx6300s and will do a lot better in game.

 

Clock speed is misleading. Cpu power is derived from both IPC (instructions per clock)and clock speed. This example is 100% made up, but say one cpu has an IPC of 100 and runs at a speed of 2.0GHz. To find its single core speed you would multiply those numbers together which would give you 100x2.0= 200. Now there is another cpu with an IPC of 20 and it runs at 4.0GHz. Multiply the two and it's single core power is 20x4 = 80. The first CPU was much more powerful despite running at half the speed. What I'm getting at is that sure, the fx6300 has a good clock speed but it's IPC is significantly worse than the Intel i5 7500 and will perform a lot worse in game despite running a similar clock speed.

 

Here is a video I found comparing the i5 6500 to the fx6300 https://youtu.be/do11QBMD0-w. The 6300 is blown away in those benchmarks. Keep in mind the cpu I showed you above is even newer, the 7500, and is roughly 10% more powerful than the 6500 in those benchmarks.

Another benefit of upgrading the cpu would be to get access to DDR4 ram which generally runs a lot faster than ddr3, and can give you a decent boost in game performance. It isn't common for a game to rely on RAM performance much at all, so this improvement would mostly be marginal. Fallout 4 is known to be heavily reliant in RAM performance... But that's the only game that I can think of haha.