its hardly the heaviest of cars tbh circa 1400-1430kg , I would imagine anything a bit on the larger side ie 4x4 ish would be fine towing this on the appropriate trailer, even something like a 5 series or a Rav4 is allowed to tow 2000kg whereas most proper 4x4s are around 3500kg bear in mind whoevers towing will need a B+E licence or to have past their test circa pre 95
We'll use my 5 Series as an example seeing as you mentioned a 5 Series.
Weight of a 2005 Avensis Estate circa 1400kg
Weight of a typical car trailer circa 700k
Total weight of 2005 Avensis Estate on a trailer 2100kg
Maximum permitted braked towing weight of 530i circa 1900kg
So even a 1600kg 5 Series is touch and go, therefore I stand by my original comment that most typical cars cannot legally tow an Avensis Estate on a trailer.
Why bother anyway? Just book it in for an MOT?