Holy hell! Attaching ANY modern video card to that rig would just be pissing your money down the drain. I'd be willing to bet that your platform is already bottlenecking your GTX 970 because your CPU was already 3½ years old when the GTX 970 came out. There is no video card upgrade that would be a good choice on that platform at
any price, period.
If you're looking at the RTX 4060, that means you have about $300 to spend (because that's what it costs). You would get ZERO benefit from it (and I DO mean ZERO) so you'd be literally pissing your money away. If you have a tight budget, that means you can't afford to be pissing your money away so I'm here to save you from doing that.
The good news is that using your $300 RTX 4060 budget for a platform upgrade instead would be a GIGANTIC performance improvement. Also, your GTX 970 wouldn't be bottlenecked anymore.
Here's what I'm thinking:
CPU:
AMD Ryzen 5 5600 (Comes with Cooler) - $150
Motherboard:
ASRock B550M Phantom Gaming 4 - $85
RAM:
32GB Silicon Power Gaming DDR4-3200 CL16 - $50
Windows SSD:
Team MP33 256GB PCIe3 NVMe - $19
Total: $304
I'm assuming that you have Windows 10 already so I won't bother with that. This setup will make EVERYTHING better, not just your gaming. You're going to be literally
shocked by how much faster EVERYTHING is. Moreover, the R5-5600 has a TDP of only 65W as opposed to the i5-2500K's TDP of 95W which will make things a bit easier on your old PSU.
The 256GB NVMe drive is more than large enough for Windows 10 and would make the overall difference between this platform and what you have even more dramatic. I ran Windows 10 for 5 years on a 128GB M.2 SATA drive and never encountered capacity issues so this 256GB drive will be good for future Windows upgrades.
This platform with your GTX 970 will out-game your platform with an RTX 4060 by a HUGE margin because your platform's gaming speed is limited by your i5. This means that NO video card would improve your gaming FPS, not even and RX 7900 XTX or RTX 4090.
I know that the AM4 platform has no upgrade path but, let's be honest here, you haven't upgraded in 12 years. Therefore, value for your dollar is far more important than an upgrade path that you probably won't use anyway. The Ryzen 5 5600 is unquestionably one of, if not
the, best value gaming CPUs on the market today and has been since its inception. It is still considered to be a top-value gaming CPU in 2023. Feel free to fact-check that statement.
Since the launch of the AM5 platform, the prices of AM4 parts have just fallen through the basement floor even though they're still perfectly viable, modern parts (I'm still using AM4 myself) and that really lends itself to your specific situation.
To give you an idea of the difference in performance between those two CPUs, here are their Passmark scores:
Intel Core i5-2500K - 4123
AMD Ryzen 5 5600 - 21645
This is the upgrade you should perform and you'll be wildly happy with it, this I guarantee!