Agreed, a Ryzen 5600X should keep you settled for a good while. Though any Ryzen cpu will also require a new motherboard. I'd suggest either a B550 or X570, since those boards are compatible with both Zen 2 (i.e. Ryzen 3000 series) and Zen 3 (i.e. Ryzen 5000 series) cpus, giving you the widest range of options. But also because they have pcie 4.0 chipsets, in case you were to get one of the new RTX 3000 series or Radeon RX 6000 series gpu now or later, since those are pcie 4.0 cards. I mean, those cards will still work fine on your current mobo, but just not as well as they could on those newer boards.
And if you go Ryzen, you might also want to swap out that old DDR3 ram for the fastest DDR4 you can buy, since Ryzen cpu's tend to perform best when paired with fast ram. But not too fast either. I seem to remember 3600Mhz is the sweet spot for optimal performance on both Zen 2 and Zen 3 cpus. Good news is 3600MHz is quite affordable. About $80 gets you 16gb. Keep it dual channel tho i.e. 2x8gb, or 2x16gb if you want to splurge.
Also, what kind of storage are you using? If you're still on a mechanical HDD, you'll definitely want to upgrade to an SSD. Another area where those motherboards mentioned above have an advantage, since they also leave room for a pcie 4.0 nvme m.2 SSD, which is pretty much the fastest storage you can currently get for pc. Tho if you're already on an SSD, I suppose you could get away with just skipping this one.
Sorry if I'm making this confusing by dropping a whole lot of tech talk on you. It's just that if you'd slap any of the new gen gpus in your current build, the disparities between it and the rest of your pc will very likely mean the gpu will be bottlenecked. Or put otherwise, you'll have put down money for power you can't fully utilize. If that is not a problem for you or you're planning on doing incremental upgrades, and you just want a recommendation? Then easy, RTX 3060 Ti, plain and simple.