For what it's worth, going from my old Phenom II X4 965 to a 6700K made a very noticeable difference in gaming performance even though I was just using a GTX 660Ti for graphics. A modern card should definitely still provide an acceptable experience, but it will be held back by the processor.
There's also the platform improvements. PCIe 3.0, DDR4, SATA 6 Gb/s, NVME storage, etc.
Going from a 2500k to a 5820k for me was massively noticeable on a 290, an upgrade ago. Phenom is not worth using any more. Get a cheap used workstation with a Sandy or Ivy HT Xeon for $250 on eBay at the very least. Even better, get the low end super cheap Ryzen or new i3 and have a really solid chip for not much $$$
