For typical home use such as connecting a router to a smart TV, a CAT 5e ethernet cable is more than adequate as the limiting factor will be your broadband speed, for HDMI over ethernet we recommend using CAT 6 full copper. An ethernet cable is graded by the speed of data it can transfer, CAT5e and CAT6 both support Gigabit ethernet (1000mbs) as well as lower speeds, CAT6 has a tighter twist in the wire pairs which allows 10 Gigabit networking over distances up to 50m and 2 way communication on each pair of wires, the tighter twist also provides better noise immunity which in turn leads to lower delay and skew. CAT6A has a further tightening of the wire twist and adds a shield, this allows 10 Gigabit networking up to circa 100m.