My current rig is in my signature. I do editing, and 144hz gaming. I have a freesync monitor on my list, and 32gb of ddr4. I was also thinking of upgrading to a 5960x.
It depends on your editing software and the settings. By the time you get a 5960x, x99 motherboard, 32gb of ddr4 ram you're looking at a hefty upgrade that would likely only be worth it if you do it on a professional level. For gaming, you might be able to outrun the opponents faster due to being lighter in the wallet 😛 . Seriously there's little to no gaming improvement, if anything games may be a bit worse due to slower core speed vs say a 4790k or 6700k. The 6700k performs a lot like the 5820k in many scenarios.
I'd consider a 5820k or if you need the additional pcie lanes, the 5930k for around $530. For the 5960x you're paying close to another $500 for 2 more cores which I don't see being worth it. The more cores typically the harder it is to overclock, you'd get more usefulness I think out of a 6 core oc'd to raise the core speed up so your gaming doesn't take a hit.