Cat-5 is an unshielded twisted pair (UTP) cable with a characteristic impedance of about 110 ohms. It was designed for balanced data/phone and not for RF applications, however it would be possible in theory to press it into service to connect an OTA antenna to a TV set.
There are 3 main obstacles. First is matching the odd impedances. The typical TV antenna does have a balanced output before the usual 300 ohm balanced to 75 ohm unbalanced balun, but its characteristic impedance is 300 ohms and I haven't seen any 300 to 110 ohm baluns at Radio Shack lately! You could wind your own if you are handy...
Second problem is noise pickup. In theory a cat-5 twisted pair rejects common mode undesired signals like electrical noise, but that only works well when the receiver has a true balanced input. The good old 300 ohm inputs on TVs went away a long time ago in favor of the 75 ohm unbalanced "F" connector, probably for good reason. So now we need a 2nd custom balun from 110 balanced UTP to 75 ohm unbalanced at the input to the TV.
Finally there is the issue of signal attenuation. Cat-5 cable is usually sweep tested and rated for use at up to 1GHz for digital signals, well above the top end of the UHF band. But it is not measured for attenuation the same way 75 ohm coax like RG-6 and RG-59 is, so we don't know how much loss a high end UHF station might have after a 100 or 200 feet run.
Having said all that, if you are adventurous, live in a fairly strong signal area, are mostly interested in DTV (digital) not analog reception, don't mind getting up on the roof (or in the attic) at the antenna, and don't have a neat or convenient way to run some more coax, it would be easy to test the theory.
Connect one cat-x pair, say blue/white, directly to the antenna wing nut terminals, folding the 3 other pairs back out of the way. Don't use any balun, and try to maintain the "twist" as close as possible to the connection point. At the TV input, use one of those old 300 to 75 baluns that come with the "UHF loop" supplied with the set to "match" the sets RF input. Doing this treats the UTP cat-x as if it were 300 ohm twin-lead, which is not an ideal "match" but for this experimentshould work.
This setup violates all kinds of good engineering practices, but because the DTV signal is very robust and forgiving compared to analog TV, I would expect usable reception from local DTV stations, and possibly from the stronger analog channels, especially VHF. Look at it this way: with DTV it will either work perfectly (excepting multipath issues, which would be the same with a coax lead-in) or not at all. If it doesn't work, it's time to run some more coax!
Have fun and enjoy the hobby side of being an AVSer.