Would this help with gaming?

Saying that your build is so dated and you have to replace motherboard, processor, and will have to upgrade your GPU as well, if you can afford it I would recommend jumping to Intel. You are mostly interested in gaming then you want to be on Intel, for now at least. I love AMD, and I have a Sabertooth 990FX and FX 8370 and love it, however I already had the Sabertooth 990FX when I upgraded so the FX 8370 was a good upgrade. Saying you need new motherboard and processor I would suggest looking for a good deal on a Haswell board and i5 processor. If you need a better deal there is nothing wrong with going Ivy Bridge either. Intel has the gaming superiority in processors for now, but there really isn't a huge gain in performance between Ivy Bridge, Haswell, and Skylake. For the cost of the Asus Crosshair V Formula-Z ATX AM3+ and FX 8350 you could easily go with an Ivy Bridge or Haswell i5 (maybe even i7) and get better gaming benchmarks.

If you really want to stay with AMD you could save a little by going with the Asus Sabertooth 990FX AM3+ board and getting FX processor. If your just gaming the go to gaming FX processor is the FX 6350 (on Sabertooth board can overclock easily to 4.5 - 5Ghz) as no game (as of now) uses more than 6 cores. If you are also doing editing or other mulit-media tasks then FX 8 core will suite you fine. The top of the line is the FX 8370 (you don't want FX 9xxx series as they are power hungry furnaces and FX 8370 can easily overclock past 5Ghz). Newer FX 8350s typically overclock between 4.5 - 5Ghz but you have more of a lottery with the 8350 than you do with the 8370.

Your other option would be to wait for a few more months and see what Zen (AMDs next gen processor) is going to be. It is slated to have a 40% IPC gain over Excavator so it will be much more robust than current FX processors. Zen is slated for release 4th quarter 2016 to early 2017 (should release close to Intel Kaby Lake).