Couple of things you said that are red flags:
l. Lots of sway
2. towing that light trailer gets 7-9 MPG
You really need to know what your GVWR of the 5er is AND the GCVWR of the tow vehicle. You really need to stay around 80% or less of the GCVWR of the tow vehicle. Dry weight does not always include things that are added after the initial body build of the 5er.
Someone commented on stoppability. I agree 300% When you are near/at/over your max, your ability to stop that rig is diminished considerably.
I think your biggest clue is poor gas mileage. I honestly don't think your TV is adequate for the job you are asking it to do.
Do yourself a favor and forget dry weight and use GVWR and CGVWR and you will find inproved fuel economy as well as being able to stop that beast easier.
PS: LE?
