Dan,
The 2005 model MDX is the last year that Honda corporation recommended a flat tow for that Acura model. The owner's manual even covers the procedure on how to do it. Recommendation is to idle the engine and go through the transmission gears for a short while, then place in neutral with the key switch in ACC every time you start towing and repeat each 8 hour interval if you to a very long session. The odometer does not even record the miles you tow, just driving miles. Of course, you are told to keep it at 65 MPH or less when towing -- which is not a bad thing to do anyways.
Beginning just a couple of years ago, Honda removed the recommendation for flat towing their CRV as well -- that little compact SUV was a very popular choice of toad until then...
Here is a link to the 2005 Dinghy Towing Guide with information on these MDX flat tow traits.
https://images.goodsam.com/newmotorh...yGuide2005.pdf