Minimum Safe Altitudes - FAR 91.119
Federal Aviation Regulation, or FAR, 91.119 states that pilots must maintain an altitude that allows a safe landing in event of an aircraft power failure. This includes maintaining 500 feet of separation between the aircraft and a person, vessel or structure, including power lines.
Careless and Reckless Operation - FAR 91.13
FAR 91.13 states that pilots may not operate an aircraft in a reckless or careless manner that may endanger the life and/or property of another. Since flying very close to power lines is an inherently dangerous and illegal act, it would constitute a violation of FAR 91.13.
Aeronautical Information Manual
While not regulatory, the AIM is nevertheless an FAA-published official document of recommendations that all pilots should follow. The AIM warns pilots that power lines are numerous below 200-feet above ground level. The AIM advises pilots to exercise extreme vigilance when flying near power lines and to constantly scan for them when operating below 200 feet above the ground.