Which one should I choose between these two, the i5‑6400 or the i5‑6600K?

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I’m in a dilemma right now. At the moment I have an i3‑7100, a GTX 1060, 16 GB of RAM, a 1 TB SSD and a 320 GB HDD, all on an H110 motherboard, powered by a generic Huntkey 450 W PSU. I want to replace my i3 with either an i5‑6600K or an i5‑6400. Now, the processor requires about 91 W or something like that. According to ChatGPT, I could use it, but it’s quite risky — things like random restarts, and it could probably affect the lifespan of the other components, and stuff like that. Can it be used?

Here’s the other part of the question: I’m being offered both for the same price. I know with the 6600K I can’t do overclocking, and I’m also worried that my PSU, being generic, might not be able to provide enough power to the CPU and it could get damaged, plus temperature could be a problem. I don’t really know the brand of my coolers because it’s a second‑hand system, but I’m almost sure they’re generic or very basic. The seller of the i5‑6600K is including a cooler and says there shouldn’t be heat issues, so I assume it’s sufficient. Which one should I go for? Thanks, and sorry for my bad English.

ps: for extra points, which one is better to play helldivers 2?