Yes, a Mazda CX-5 can tow a small caravan, but how small depends on year and engine.
Typical Australian figures are 1,400–2,000 kg braked (many petrol models around 1,800 kg, some diesels up to 2,000 kg), 750 kg unbraked, and about 150 kg towball download.
Mind your GVM/GCM, payload and towball mass—add family, gear and water and your margins shrink faster than a budget esky.
Lightweight pop-top or compact caravans (roughly 1,200–1,600 kg tare with modest ball weight) are the sensible match; chunky full-height vans are asking a lot.
Fit a quality brake controller and towing mirrors, and check your CX-5’s exact ratings in the owner’s manual or door jamb; you’ll find plenty of suitable lightweight caravans on Tradingpost.
Consult official documentation for exact figures.