How should I connect the audio ground and shield wires in a Cat5 cable for analog audio?
You can treat the 4- twisted-pairs inside a standard CAT-5 cable as simple unshielded twisted pairs for audio applications.  If both the sending end and receiving end are fully balanced, you don't need to do anything else.  You can try using the 4th pair as a ground conductor but even that is not normally necessary.

On the other hand: if either the sending end or receiving end are un-balanced, you will need to play around to see what works for you.  I would normally insert audio balancing transformers at the receiving end - this works well even in the presence of significant common-mode noise.

I use CAT-5 cable to connect RTS Adam Intercom Panels from remote locations back to the Intercom Frame.  A standard Adam analog port uses 3- pairs: balanced audio to the frame, balanced audio from the frame, RS-485 data for key-panel data.  Even with cable runs that exceed 2000 feet, I find that I don't need a ground conductor between the Intercom frame and the key-panel.  My concern, of course, is keeping the RS-485 data transceivers operating within their common-mode range.  Just hasn't been a problem - ever.

In your situation (short cable run within a single room: I wouldn't expect any problems whatsoever.  This assumes that you are talking about balanced audio signals.  I'm making that assumption because you are talking about using standard mic cables with XLR connectors.