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.

A tutorial on how to use RJ-45 UTP cabling for video transmission and camera control as you migrate toward IP-based wiring An illustration shows a suggested format for connecting analog video ...

Belden 1872A MediaTwist Cat 6 cable. Last month, we covered unshielded twisted pairs (UTP) to carry audio. The highest-quality UTP is computer cable, premise/data cable. It's called Cat 5, Cat 5e or ...

Coaxial cable: Coax is good for short wire runs in low-noise environments. Its thick copper construction yields low signal losses. As an unbalanced transmission-line, its interference immunity is poor ...