Nope same AMD 5600X. One give kelentong story same like yours. Stock cooler is fine if no OC. I bought the one with the cooler.

For the high end CPUs, read that Nvidia and AMD have stopped including stock coolers for these.

Will be interested to know if you can find sellers offering stock coolers for these high end CPUs.

For lower and mid CPU, maybe some have stock coolers included in the package.

What is considered is high end CPU? i don't think 5600X can be considered high end, most, mid-range. Seller tipu with this kelentong story.

High end - threadripper

Mid - 5900X (this one does not have stock cooler)

Find out from AMD whether 5600X has a stock cooler or not. If ada and seller says tak ada, then tipu.

There ARE so called "fake" CPU in the markets

the scammer will usually delid the CPUs, swap the IHS of the old one with a new one, for example a CPU IHS there stated it's a 5950X, but it might be just a 1200 underneath, you wouldn't know until you've booted it up

But fake delided CPU for AMD is pretty rare compared to Intel as AMD soldered their IHS, making it extremely difficult to delid
Another method the scammers used for AMD CPU is sanding off the labels on the IHS, and print a fake label as higher spec CPU

AMD CPU comes in with a box and without a box (in plastic casing).

Only the one in box is original?

How to tell if it is original?