Worth the $800?

That is money well spent. I would recommend a Asus 7850/7870 for the GPU. A 7850 will run in the same price range as those, 7870 will go for a bit more.

For the CPU, I would probably save up 70$ and buy the i7 3770K.

I would go with a GTX 680 if you have the dough, but a nVidia 580/570 is a sure choice and will serve you greatly. I agree with Gaming, i 3770k. I would research hyperthreading, that's the difference between i7 and i5. (Some you know, more GHz, etc.)

For Gaming stick with i5-3570k, you don't need hyperthreading at all, and it saves you at least $70 that you can spend on something else

Asus Sabertooth's are awesome boards, worth every penny if you ask me.

Mine obviously is an AMD one, but the principle still holds true. The only regret I have was that I didn't go for the big 1100T 6 core instead of my 975 quad core. Not that the 975 hasn't done well for me, but in my opinion whether your need the performance of not, this is the varsity year for the LGA 1155 socket, I say get the best CPU the budget allows. But yes, its correct, for gaming there is absolutely no advantage of the i7 over the i5.