Too many Lawyers...
This has been covered pretty well on this forum... but to repeat because it's worth repeating...
Yes, at least two manufacturers make a bolt on hitch for the Mazda5
Yes, the car, from an engineering perspective, is more than capable of towing a small load, at least 1,000 lbs with no trouble, but I can see where it might have trouble with the full 2,500 lb capacity of a standard US Class 1 rated hitch.
But, Yes, you will void your warranty if you put hitch on a Mazda5.
It's a case of too many lawyers and Insurance companies wanting to limit their liabilty, and the US truck makers controlling the hitch class ratings so that you have to buy a truck if you want to tow anything.
I plan to get a hitch on my 5... but only once the warranty expires.