Putting Ethernet cables alongside power lines isn't the best decision ...
A. Cables or raceways run parallel to framing members or furring strips must be protected by installing the wiring method not less than 1¼ in. from the nearest edge of the framing member or furring ...
It's perfectly safe to run Cat5 parallel to power lines (or any other EMI source). The twisting of the wire pairs cancels out almost all interference.
I'm running wires to my new addition, several feed Romex cables and several Coax cables from a Dish Network multi switch. Will the coax pick up interference from the Roxex? Are Dishnetwork lines ...