Some of the comments here are utterly WRONG and will just mislead you. As someone who uses APU's and did an extensive research with benchmarks, listen to me carefully and decide.
To cut the story short, GO FOR THE AMD A10! It is WAAAAAAAY more powerful than the i5 IN TERMS OF GAMING (which is your sole purpose).
Now you need to understand something very important. You are talking about two APU's (the i-Core and A-series processors are APU's). An APU is a processor that has an integrated Graphics Chip (CPU + GPU combined). Therefore, it is assumed that you are not planning on buying a dedicated graphics card. If you plan on buying a dedicated graphics card then why on earth would you buy an APU?
Now if we're talking about APU's performance in GAMING, then the A10 would even beat the i7 (but perhaps not the $1100 i7, the latest one, I do not know its gaming capability, but you're seriously not planning on buying that overpriced chip, right?). Even my old A8-7600k can play Crysis 3 smoothly on med-high settings, non HD, on a friggin slow 1600Mhz RAM. The i5 can't do this. This is because the i-Core series have lame graphics chip, they focused on the raw power of their CPU which is indeed better than AMD's CPU raw power. But APU's are for GAMING purposes, that's why it includes a graphics chip obviously, so the only thing that counts is their gaming performance. If I want raw CPU power, I would have bought an AMD's powerful OCTACORE processor for a still cheaper price than i5, and then I'd use the spare money to buy a graphics card.
And someone even said that the A10 will cost more in the long run because you will have to get a fast RAM (2133Mhz RAM) and a good cooler. This is a terrible misinformation. You need a fast RAM whether you go for i5 or A10. But the good thing about the A10 is that it would benefit much greatly with a fast RAM but the i5 barely would (i5 has a LOCKED memory size and slow clock speed, the A10 uses system RAM so faster RAM means faster A10). As for a cooler, there is no need to overclock the A10 since it is way more powerful than the i5. Only the i5 needs overclocking to catch up a little. But here's the best thing about the A10-7860k: it comes with a free cooler!!! You can now overclock its iGPU to around 1000Mhz to significantly increase your FPS to further beat the i5 into a bloody pulp.
So please, I hope I'm not too late, be a wise buyer. Intel is overpriced yet AMD delivers more power at a cheaper price. Without AMD, Intel could freely rip us off.