I'm surprised people will say no problem when they have no idea what the tongue weight is or what that truck is capable of or how it's equipped. If he's been towing a 5K lb TT, maybe it's a 1/2 ton. New 37' trailer could have a tongue weight up around 1500 lbs and receiver and WDH rating could be significantly exceeded. His existing spring bars aren't going to transfer much wt. back onto the steer axle. Accidents can anytime, anywhere, at any speed. I'd say no.
I would tell the dealer your truck isn't capable and you're having trouble finding someone to tow it and it may be a couple of weeks before you find a tow. They won't want it hanging around very long and it could be gone by tomorrow. My DW would have made them do it as part of the purchase contract.
