I don't think I would but have goggled a couple that have, read the past below.
So, can you flat tow a 2014 (or 2013) Mazda CX-5 behind a motor home?
The short answer is, "No."
A slightly longer answer appears on page 3-53 of the 2014 Mazda CX-5 owner's manual under the heading Recreational Towing.
"An example of "recreational towing" is towing your vehicle behind a motor home. The transaxle is not designed for towing this vehicle on all 4 wheels. When doing recreational towing refer to "Towing Description" (page 7-20) and "Tiedown Hooks" (page 7-21) and carefully follow the instructions."
That's it. I've left nothing out. No distinction is made between the six-speed automatic and the six-speed manual transaxles. Likewise it doesn't appear to matter if the CX-5 in question has front-drive or all-wheel drive.
The pages on chapter 7 refer mostly to the sort of recovery towing done by tow trucks, but the text here does make it clear that the front-drive CX-5 is good to go with its front tires on a tow dolly. As for the AWD version, well, bring a trailer.
But tow dollies are just malformed trailers. The front-drive version gains little here.
Let's face it. The Mazda CX-5 is simply not for you if you want a car to flat tow behind your motor home. Pity. It's an otherwise nice machine that ticks many other boxes on an RVers wish list.
Dan Edmunds, Director of Vehicle Testing @ 2,343 miles
Walt & Will
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