If you have the cat5 cable going directly from the bedroom to the receiver location you could use what is known as a balun.
This will use the cat5 cable exclusively for video though (no network) and it must be a direct run from the source to the destination (no hubs/switches/routers, etc.).
They look like this:
http://www.gemelec.com/compvideo.htm
One issue is that on a single cat5 cable you can only run the component (for HD video) and digital coax audio. If your TV does not have a coax audio in (single orange RCA plug), you will need to find another solution for audio as you cannot run standard RCA (red and white) audio with component on a single cat5 run via baluns.
This will use the cat5 cable exclusively for video though (no network) and it must be a direct run from the source to the destination (no hubs/switches/routers, etc.).
They look like this:
http://www.gemelec.com/compvideo.htm
One issue is that on a single cat5 cable you can only run the component (for HD video) and digital coax audio. If your TV does not have a coax audio in (single orange RCA plug), you will need to find another solution for audio as you cannot run standard RCA (red and white) audio with component on a single cat5 run via baluns.