To get that FPS for the next five years you'd need something slightly beefier, assuming you purchase brand new games and want them on max settings.

If you're like me and ok with turning shadows to medium and ambient occlusion, etc. Off entirely, then you could probably squeeze a 3070ti for five years but a 3080 would be a good choice too. I prefer Nvidia graphics because they're more established and AMD is still catching up on certain technologies, but AMD CPU's have come a long way and are absolutely the best bang for your buck, and while I'll get downvoted again for speaking the truth, you don't need an AM5 socket for gaming performance and IMO it's all overpriced still. Stick with AM4 and snag a last gen Ryzen 7, that'll help keep your other components lower in price. Unless you're doing video rendering you simply don't need a very robust CPU. Almost every model in this thread would be three to four times as powerful as you need and would massively overload your budget.

Don't skimp on PSU but you can get a good one for 80-100USD from a reputable brand like Corsair that would fit your needs (850-950 watt.)

So far I haven't seen anyone actually pitch you a build that does what you need at the most reasonable price, they're just overloading you and then claiming you can't get the performance you're asking for at the price you want.

I have a PC at home that says otherwise, your downvotes mean nothing to me.