Try here
https://thebottlenecker.com/calculator
You can buy the latest greatest GPU made, but it can still be choked by not having enough CPU or memory.
Plug in what you have then see what GPU matches your hardware for best performance and/or see what you might need to do to get the most out of a GPU you might be thinking about.
I looked at both a Core i5-3470 and a Core i5-650
Both look to be inadequate for VR
HTH
Looking at what you've posted so far, I'd really suggest you save up for a new system you can purchase that will do what you want. VR takes a lot of horsepower in a well set up system. In that you seem very inexperienced in what you need to know in order to do proper hardware upgrades, I think you'll be terribly disappointed at the outcome if you attempt to upgrade your current system. As has been pointed out, "a Core i5" hardly describes the CPU considering all the iterations of Core i5 available. Memory is similar in that you could have DDR3/DDR4 running at one of a wide range of clock speeds, all of which affect performance. Motherboard chipsets are a whole nother issue.
A really good PC build matches hardware so that the integrated build gets the most bang for the buck and will last well into the future. It's not as easy as it sounds unless you really get into the details of specific hardware configurations.
I've been postponing a new build for 3+ years as I didn't see a confluence of technology affording the opportunity to get matching hardware that was new technology. It appears that the next window will be late summer when AMD's Zen 2 tech arrives with PCIe4 and hopefully some reasonably priced video cards. So when the tree is ripe I'll be looking at M.2 SSD, Zen 2 Threadrippers with 64 PCI lanes and probably a 2080Ti and 64GB of DDR4.
If none of that makes any sense to you, you'd be better served saving up for a professionally built system that will do VR OOB.