Honestly for your price range, I'd go just as stated above. Grab an AMD Ryzen 1600 6 core with SMT(think hyperthreading) and a B350 series board so that you can overclock.
I had an FX 6300 previously. The 1600 is a nice upgrade. For single core perfomance, it's on the level with intel haswell cpu's. But for multitasking, it even does better than the i7 cpus. I had mine overclocked to 3.7ghz on stock cooling, but I just changed the cooler, maybe I'll try to go higher who knows.
But all that said, for games or application that are single threaded, the intel will have a slight advantage. However, when you start doing more than just gaming or if you do multiple things at once, the 1600 is going to throw down. It's not a slouch for gaming either. The 7600k is what like 10-15% faster on single threaded? So you are a talking a few frames, but if you are on a 60hz monitor, then you won't see the difference of say 120 fps vs 110 fps.
Other bad thing going intel right now is coffee lake comes out in like a month. I'm not sure that the current motherboards will work with the new coffee lake cpus. So if you drop the money on i5 now, for a quad, in a month they are supposed to release 6 core i5 cpus(no hyperthreading), but if the board you buy today won't support a newer cpu, you are out of luck. Rumor is the new i3 will be quad core, so your i5 is basically a fast i3 at that point.
If memory serves, the socket am4 that Ryzen is on is supposed to be supported until 2020, so you may be able to go with Ryzen, then drop in a newer cpu in a couple years or so, as it looks like they will bringing out improved versions later as well.
This link should give you an idea.
http://www.eurogamer.net/articles/digitalfoundry-2017-ryzen-5-1600-1600x-vs-core-i5-7500k-review
Keep in mind, most games/software is optimized toward intel currently, so if Ryzen is already doing this well, if developers begin to optimize more for it as well, then it should get a bit better as well.