Included cpu cooler spec

Intel.com i5 6400 & i7 6700 states the included Thermal Solution is E97379, so you can run that through google & find its size, compare it to yours there. I see that this cooler may have part# E97379-001 & is used over several platforms / sockets; my guess is you have a basic i5 / i7 fan-sink; any upgraded heatsink should be socket 1151 compatible, & be mindful if the new part will simply attach or if it needs the motherboard removed to accommodate a new back-plate. I don't have a Skylake board so can not say what needs to happen there; a member here that purchased a non-K with basic fan-sink was able to install a liquid cooler by simply bolting it on without messing with the rear backplate; you'd 1st try to bolt it on, & if it's a no-go, remove board / install new backplate / reinstall board + new cooler then see what happens when psu caddy closes. I have a feeling all / most 1151 heatsinks will be a simple drop-in. Be sure to apply thermal grease on CPU 1st, if new part does not have any on it (Arctic Silver / Gelid / ICD / Grizzly etc), I hope this helps