Hello,
When I bought my 2016, my research indicated the trailer prep pkg included just basic wiring to the back which was true, present were harnesses for blinker, brake, and tail lights. I had planned on having a brake controller installed which through limited experience has proven absolutely necessary. Sound like your dealer was poorly informed, or mislead you but the car seems to be equipped as Hyundai intended. The 5000lb capacity is if you use weight distribution so it is needed. Our RV dealer said the typical unit they use was too heavy so they installed an Equal-i-zer® 400 / 4,000 lb which is much lighter, it included sway control and has worked very well.
Too bad about your test run but my experience so far has been great, our trailer is about 2900 empty with <300lbs tongue weight, obviously that changes as you load but we have had no trouble. The car pulls impressively with the load being no more than 3300lbs. I think it would do well with 4000 but would struggle under a full 5000. The horsepower is high but the torque peaks at about 5000rpm so you'll likely pull big hills in lower gears at higher rpms. So far we have had 2 trips at less than 40 miles round trip, fairly flat with no issues. Last week was 150 miles round trip, in I80 in western Iowa with steep hills, but no longer than about 1.5 miles. I was able to pull every hill in 4th gear at less than 4200rpms with one exception dropping into 3rd gear, 50 mph and 4500rpm. Great power but the torque is just a little behind. I have yet to decide whether the auto trans shifts better on it's own, or if I do better manually shifting. The chasis feels truck like when pulling, I will consider adding air bags to the rear springs for stability but it really doesn't need it at this point, I think they'll just make it feel a little less bouncy but the weight distribution should handle the weight. All said, it is a very good tow vehicle at 4000lbs and under.
As for the tranny cooler, my research indicates it has one but likely pretty small. I have a trusted mechanic who has a trusted tranny partner shop, the verdict they gave was that a 2nd cooler is always good but the factory unit should be good with my relatively light load. They suggested revisiting the issue if I begin towing on extreme, extended hills or in the mountains. I am going to look for gauges to monitor the oil, trans, and coolant temps, if the trans seems risky I'll add a 2nd cooler.
We picked the Santa Fe because we have a situation that does not allow a pickup truck, and it was preferable to a domestic SUV in size, price, and personal preference. You should do well.
Hope this helps. Good luck
