Is my router compatible with a cat5 or cat6 ethernet cable?

[Doppelganger_1]

I have a Netgear Nighthawk X4S-AC2600 4x4 MU-MIMO Smart Wifi Gaming Router R7800-100NAS.

 

[kanewolf]

Sure. Cat6 or Cat5e will both be just fine. Original Cat5 is not common any more and should generally be passed in favor of Cat5e if you are buying bulk cable. Premade cables, you may as well get Cat6.