pentium4inside :
the 8350 won't bottleneck the gpu but i would recommend you to upgrade your ram to 16gb.
and for the mobo, you mean the ASUS M5A99FX Pro R2.0 right? not M5A99FZ!
That's flat out incorrect for the CPU. (mixed feelings about the RAM upgrade as I have 8GB but have never, ever actually needed it for any game provided I don't have a web browser running)
The FX-8350 can and will bottleneck the GTX970 in many, many games. Sometimes you'd get over 40% higher FPS with a top-end CPU. (I've seen over 60% better in some games with similar GPU. not kidding)
This is only with a GTX580 (GTX970 is probably 50% faster or so), and these older AMD CPU's are already insufficient:
http://www.guru3d.com/articles_pages/core_i7_4770k_review,23.html
It's just an example, and of course there are games the FX-8350 should do very well in. DOOM for example is pretty well threaded now in VULKAN, and I think the Battlefield series does a pretty good job.
Now I'm not saying it's a poor choice considering his budget. It's not, and of course if it gets him to 60FPS rather than say 45FPS and that's all he wants then great.
OTHER:
Adaptive VSYNC is a great tweak for some games. It auto turns VSYNC OFF to prevent stuttering if you use VSYNC but can't maintain the cap (60FPS for 60Hz monitor). Here's an example:
a) run game but note constant drops below 60FPS even after trying to tweak game settings
b) VSYNC OFF
c) NCP-> manage 3d settings-> program settings-> add game-> Adaptive VSYNC -> SAVE
d) FPS counter in game should stay mostly at 60FPS (aim for 90% or so locked by adjusting settings) but if you drop below you should get a little screen tearing rather than stuttering
*This helped me a lot for Assassin's Creed games as they dip a lot even on a top-end system.