Personally, I would not attempt to use unbalanced CAT-5, but as others have pointed out, sometimes you could get lucky. One worry for me is that the ground loading could change over time and you'll develop a (potentially intermittent) hum at a later date. One scheme that hedges against hum (somewhat) would be to use three pairs in the CAT-5. Use one pair to bond the chassis together, then ground one wire in each of the signal pairs -- at one end only.

In any case it is very important that the CAT-5 be driven from a low impedance source. For example, a Sonos CONNECT would be a good choice for the driver because it's output impedance is uncommonly low. (You can easily drive headphones from this output.)