There are likely to be problems with the video and sound. The first problem is that the Cat 5 cable is a different impedance to the video signal. Normally video runs on 75 Ohm coax and Cat 5 has a much higher impedance. This could result in ghosting(electrical signals reflecting inside the cable) in the video signal. There are adapters that allow the impedance of the video source to match Cat 5 cable. I know Jaycar electronics here in Australia sells these adapters(though they're not cheap). You aren't going to have a huge run so you may be okay. The other problem is that the audio and video signals are unbalanced. This means they will be very easily affected by electrical noise in the unshielded cat 5 cable.
The only way to see if using it is acceptable is to try it. If there is too much noise or reflection you will need to use balanced differential drivers for the audio and video and it probably isn't worth the trouble.
[ 07-22-2001: Message edited by: Technics ]