It's going to depend on price, but if you want to replace your i5-3500K, your best bets are the i7-3700 (same cores/core speeds, locked so you can't OC it, but you get Hyper-Threading capability), the i7-3700K (slightly higher core clocks, plus you can OC it), or at least a Xeon E3-1275 v2 (same speeds as the 3700K, trades the iGPU for a slightly cooler running temperature -- not that you need that with the R9 390 -- & you lose the ability to OC it), or even a 1280 or 1290 v2 (slightly faster core prices).
Again, though, it depends on what's available & what you're willing to pay. On pcpartpicker.com, for example, the Xeon E3-1275 V2 is running just over $400 (~$350 for the "OEM/tray" version, but I don't know how that differs from the non-OEM option), while the i7-3700K costs another $160. For those prices, you could get a decent Skylake i5, new motherboard, & DDR4 RAM, & be set for a long time (just remember to set aside time to back up your files & reinstall Windows).