Which cpu cooler should I use for i5 6500

The stock cooler should work if you're overly concerned about it. Otherwise a smaller air cooler should be plenty. Something like a cryorig m9i would be plenty. It's smaller than the 212 evo, a bit lighter, cools a bit better and it's quieter.

http://www.newegg.com/Product/Product.aspx?Item=9SIA4UF39E2338&nm_mc=AFC-C8Junction&cm_mmc=AFC-C8Junction-PCPartPicker,%20LLC-_-na-_-na-_-na&cm_sp=&AID=10446076&PID=3938566&SID=

Since it's a locked i5 I wouldn't expect it to get too hot.
 

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That looks really nice man, i never seen that before. it has a nice look.
 
Your i5-6500 should have come with a stock intel heatsink. That'll work for what you're trying to do but an aftermarket one isn't a bad idea. The CRYORIG M9i like Synphul suggested is a good one, and if its not available in your area the ol Cooler Master Hyper 212 Evo is also a good pick. Personally I prefer the mounting system the Cryorig is using but both will do the trick for you.

As for the skylake mounting issue, its hard to say exactly the cause since everyone's reposting the same articles. In general the concern is high pressure mounting systems, and in the one case by MaximumPC it was having a screwed up mounting plate that allowed the cooler to be over tightened. While the Skylake cpu's are thinner than haswell/broadwell, using a normal mainstream cooler shouldn't be a huge concern. Just make sure you're not trying to squeeze blood from the screws when you mount it.
 
The Cooler Master GeminII M4 isn't going to cool as well. However it will work, tho I've heard the non ver2 models have vibration noise issues.

Where are you searching that the CRYORIG M9i and Cooler Master Hyper 212 Evo are out of stock?