I take it you are aware of the frequency and power output requirements for a video amplifier?, you can't just use any old opamp.
It makes it more difficult because the 'virtual earth' method requires capacitor coupling, and to drive video into 75 ohms requires a large value coupling capacitor.
Are you sure the cable isn't faulty?, or the wrong type?, 5m shouldn't be a problem?.
Funnily enough we've just fitted a reversing camera on a van at work, but it's wireless - really cool thing, and only cost about £50 for camera and monitor.