AM4 or AM5 for a complete gaming PC upgrade?

I'd pay the extra for AM5 here. You're already buying a motherboard and RAM, and the 7800X3D gives you more CPU performance now as well as a newer platform to work with later.

That doesn't mean you'll never need another motherboard. A future CPU upgrade depends on board compatibility and BIOS support, and you might keep the 7800X3D long enough that a socket upgrade makes more sense anyway. Still, for this particular price gap, I'd rather have the option.

AM4 can still make sense if the $260 difference matters more to you than a future CPU swap. The 5700X3D is a capable gaming chip, and moving to 1440p can shift more of the workload toward the GPU, though that varies a lot by game and settings.

I'd be less enthusiastic about this specific deal, though. Paying $361 for a used processor is a different proposition from finding one cheaply. Check the seller's return policy and factor in the risk before treating the savings as a sure thing.

Don't choose based on the socket alone. Look at benchmarks for the games you actually play, especially at 1080p if you're keeping that monitor for a while. Average frame rates and low frame rates can tell different stories, and the gap between CPUs won't be the same in every game.

Also check whether a cheaper AM5 processor and compatible board would give you the performance you need. That might bring the platform price down without paying for the 7800X3D, although it won't solve an inflated DDR5 price.

There are Intel options worth pricing too, such as a 13600K or 14600KF with a DDR4 board. Compare the full cost of the CPU, board and cooling rather than just the processor price. Reported reliability problems with some 13th and 14th generation chips are worth researching if you expect to keep the system for many years.