A balanced gamer will budget about 2x the cost of the processor for the graphics card.
Either processor seems right if you are looking at msrp prices.
Unfortunately, both the ryzen 5000 series processors and the 3000 series graphics cards are hard to buy anywhere near msrp if you can even find them at all.
For gaming, the 5600X would be the superior gaming processor because of the better single thread performance. But, not so much better that it is worth a big price premium.
Unless you are in a hurry to build, I would wait a bit for graphics prices to calm down and also to see what intel rocket lake brings next month.
Leaked benchmaks indicate even better single thread performance than the 5000 series cpu's. Hopefully, there will be sufficient suppply to get some price relief.
Both overkill and overpriced for only gaming in my opinion.
A 10400F paired wtih 3070 is a really good pair.
Also is cheaper:
PCPartPicker Part List
CPU: Intel Core i5-10400F 2.9 GHz 6-Core Processor ($164.99 @ Amazon)
Motherboard: MSI MPG Z490 GAMING PLUS ATX LGA1200 Motherboard ($169.99 @ Best Buy)
Memory: Corsair Vengeance RGB Pro 16 GB (2 x 8 GB) DDR4-3200 CL16 Memory ($94.99 @ Amazon)
Total: $429.97
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2021-01-26 10:11 EST-0500
10400F falls behind 5600X in gaming by only a few fps (5-10).
8 core 16 thread 10700K is also overkill for only gaming in my opinion.
I choose a Z490 motherboard so you can achieve that 3200MHz,it might give you slight fps increase in some games,although it will be nice to have if you upgrade to a 11th gen CPU down the line.
Stock cooler will do,but a aftermarket cooler isnt a bad idea.