Some pretty good prices on these two popular AMD Ryzen CPUs if you're looking to buy right now. In terms of gaming the difference between the two is about <5% with the 5600X being better value for performance, but the 5800X is more future proof by offering more cores/threads.
5600X offers 6 cores, 12 threads with a base clock of 3.7GHz, boost clock up to 4.6Ghz and a Wraith Stealth cooler, while the 5800X offers 8 cores, 16 threads with a base clock of 3.8GHz, boost clock up to 4.7GHz and no cooler included.