For most users I don't think so
You need to consider that unless you are playing games on a high refresh-rate monitor the GPU is the very main limiting factor in performance.
In other words, when you are pushing the GPU to the limit the differences between CPU architectures and clocks are insignificant. Only very low clocked CPUs or 2 core CPUs will be an important bottleneck on your rig
However when you low down the graphics and resolutions in order to archieve higher framerates the GPU is not being stressed and the CPU makes a more substantial difference
But it also depends on the game, some games such as watch dogs 2 or GTA V do benefit for higher architectures and clock so they might be a small bump in performance with a current CPU but other games such as Tomb Rider or Rainbow will run just fine with almost any CPU even when the GPU is not stressed.
Here they compare the 2500K oc'd to 4.5 GHz (A 2500K at stock speeds should be a little bit worse than your i5 3570) against the 1500X at 4 GHz and for the most part they are pretty close to each other, there were few games that actually took advantage of the higher core-thread count and newer architecture found on the ryzen CPUs though they were mostly CPU bound scenarios when your target is 60 FPS it really doesn't make much of the difference.
MY CONCLUSION: Yes, as expected ryzen 5 cpus do perform better, but is ist worth it to change mobo and RAM besides CPU? If you play at 120 hz and above yes, for sure.
If not, I find it difficult to do, I'd wait for a ryzen upgrade that can OC higher
Maybe the minimum framerates could make the ryzen 5 CPUs look more compelling but like I said considering you have to change the entire platform I'd like to see more than that. Don't get me wrong the ryzen 5 chips are amazing CPUs and if you can afford it there's nothing wrong with them but even still, Why spending so much money if not needed?
https://www.youtube.com/watch?v=2xRAACegBzE