It might be possible to use an unused pair of the cat5 cable to transmit information that wasn't meant to pass down that cable, but you'd have to split the pair at both ends, and the sending end would need a tuner card. The receiving end could have the pair go spliced into an RCA jack and go into the Video In on the video card. This assumes a couple of things though. 1) An RCA cable only uses a pair of wires to transmit it's data. 2) The sending computer has a Video Out jack that can send 1 discreet channel of video. 3) The receiving computer has a Video In jack. 4) You only want video and not audio. 5) There isn't any interference on the "unused" pair you've borrowed from the cat5 cable.
Considering the amount of effort companies like Monster put into building RCA cables and the like, chances are you would have WAY too much interference to get a usable pictures if you had a resonable length of cat5 between the two machines. Also, considering there is data on the other pairs of the cat5, you're going to have to deal with crosstalk as well.
Also, the OP probably wanted audio with his TV, so just passing the video isn't terribly useful.
As for cable being 10Mbps... yes, cable internet usually uses a cable modem that has a 10Mbps interface on it, but that doesn't say anything about the bandwidth of the cable being used. As has already been pointed out, there is a huge spectrum in use on that cable, holding many channels of analog and digital data.
In order to stream television on your LAN, what you will most likely need to do is get a computer with a TV tuner in it, and then get some software that will allow you to stream the content obtained from the tuner card. I haven't attempted this in the past so I can't offer any concrete suggestions, unfortunately. With this solution, you're only going to be able to stream 1 channel from the cable at a time. This will be the channel that the tuner card is tuned to. You can change the channel (remotely through software should be possible) but anyone watching the stream will be switched to the new channel. If you wanted to stream multiple channels, you'd need multiple tuner cards, and possibly multiple machines to do the decoding/encoding and streaming. I have no idea how much bandwidth would be needed to move this much data (TV resolution video and stereo audio) across a network. It would most likely depend on what method you used to stream the data. If you compress it first, you would save bandwidth but require more processing power/time.
Anyhow, just a couple of thoughts. Hope it helps a little.