You can definitely overclock your i5-2500k. The slippery slope argument doesnt hold much weight here. The 290/390/970 is the sweet spot. Going above that level gets you diminishing returns. Going below that level gets you diminishing returns (e.g. price only goes down a little but performance goes down a lot). It's the current best point for good performance without getting too spendy.
An overclocked 2500k is perfectly fine for a 390. I just upgraded from a machine like that and you can max everything except very few games at 1080p. All you'd need is a better CPU cooler than the stock CPU cooler. Then google "2500k overclock guide" and follow the steps. Look into the Cryorig H7 or Coolermaster Hyper 212 Evo coolers, they are very inexpensive and a huge step up from the stock cooler. Getting to 4.2-4.4ghz is nearly guaranteed those 2500k's overclock so well. A good number of them could do 4.5-4.8 on better coolers, and 5.0 ghz+ on high end cooling. I doubt you'll have any trouble reaching ~4.3-4.4 following a guide with a 212 Evo or equivalent.
Overclocking the 2500k is literally this simple for the lower-end overclocks: Set VCore to 1.25, set CPU Multiplier to 41. Does it work? If yes, set to 42. Does it work? If yes, set to 43. Etc. until you get one that doesn't work. All you need to do is load up a program called OCCT and run it for 10 minutes at each multiplier, then play some games and use it at that multiplier for a while and see if it craps out. Once you get one that craps out, go back 1 and test that multiplier setting more thoroughly by using it for a few days as you normally would. If you still get crapping out or errors, go back 1 more and you're done.
A 390 on a non overclocked 2500k wouldnt be as good as overclocked obviously, but you'd still get a decent amount more FPS than a 380x, and a lot more when you're GPU limited (e.g. max settings, anti aliasing, high resolution, etc.).
But if this is a work computer, I wouldn't overclock