Wire Length Restrictions on Simple Battery Powered Circuit
For 50 ft, your #22 CAT6 cable should be fine.

The resistance of #22 wire is about 16 Ohms per 1000 ft, or 1.6 Ohms for your 50 ft there-and-back. The wire will only carry 20 mA or so for a standard LED, giving a voltage drop in the cable of 0.03 volts.