RS5, at least the B8.5 uses a shaft driven A/C compressor with the driveshaft coming off the rear of the engine accessorie drive and into the back of the compressor. I normally do my own A/C charging as I have most of the fittings, manifold gauges, vacuum pump. I couldn’t figure out how to engage the compressor on the RS5 to fill. I vacuumed it and did an initial liquid 134A fill and then tried everything to include Vagcom to get the compressor to engage? Anyone work on one before?
Part 2
I took it to the dealer as I needed an alignment anyway since redoing the suspension and engine install. Dealer mechanic said all the sensors checked out, valves opened and closed. He vacuumed the system and did a pressure liquid fill by weight to proper quantity and couldn’t get the compressor to com on so he says it must be bad. I can’t live with everything else checks out and the compressor turns but it must be bad? Tried to quote me 16.5hrs labor + parts for $4900. Tried to make me feel good by saying it’s actually only about $4500 after my 10% discount 
I haven’t done a ton of work on A/C systems but on the Audi The 4.2 S4 has a flawed system where the compressor goes bad on all the cars. and if you own one and use the A/C you’ve changed a few of them… best I know most if not all Audis drive the A/C off the chain drive system off the back of the motor.
It sounds like you’ve done the obvious output tests to see if you can get the clutch to engage. Check the overall system pressure because the compressor won’t kick on if a few min requirements are not met.
If you can make sure there isn’t anything wrong with the shaft drive if you can see it. You can always try to power force the clutch by feeding the green wire connector that is connected to the compressor itself.
Thanks, the dealer supposedly did a pressure fill to 550grams which is what the tag on the car shows so I’m assuming the quanitty is right. Before I took it there I was trying to do it myself but I couldn’t find the low pressure switch and the Compressor is in there so tight I couldn’t fish for the clutch wire as hot wiring it to fill, and now to check the operation is my nex goal. I guess I need to backtrace that wire in the diagrams and find the connector it goes to, then I can hotwire it. If not I’ll have to drop the whole engine cradle to swap out the compressor, I’ve heard they had issues with the shafts so I might swap the shaft too. That short 6" long shaft is $150 new.