the previous owner of my car installed headers, replacing the exhaust manifold where the O2 sensor usually is. Now, it is down after the two pipes join, about 2-3 feet from it's original location, and it's not connected to anything. I kind of want to hook it back up, unless there's any reason to leave it unplugged.
Hooking up the o2 sensor would help gas milage a little, wouldn't it?

 

according to the S4 FSM the wire is Green with yellow stripe... located somewhere near the exhaust manifold/intake manifold... it is only one wire. Don't know about the S5

and it might help a little by leaning the mixture out a little... without the O2 sensor the ECU should fall into fail safe mode and run on the rich side

 

Its a single connector on the back side of the Throttle body, by the fire wall. Did that diagram help for your PD?