This is a bit tough. Before I even answered I would ask and am under the assumption that you are gaming at 1080 at probably high settings?
In games that aren't core intensive you aren't going to see a significant improvement with any of the current Ryzen over that chip with your current card. Benchmarks seem to bear out good frame rates being had with many titles on the R3 variants at the 1060/580 GPU level. Things that are core intensive will make a bit of difference, but you also start running into how much GPU you have.
So, to the point, I wouldn't spend the money on an R5 over what you have. I am not sure a new R7 would be worthwhile with the GPU. I am sure you would see improvement, but at what cost?
If you were looking for cheapest possible, try and catch that R7 1700 ~$180 deal that's been peeking around. The Ryzen refresh is still too high in cost to offset the small perf boost IMO.