If he's been barefoot for 5 weeks and is sound, I don't see the issue with riding in the trailer and spending a little while in the arena barefoot. I have transitioned many horses to barefoot, and 5 weeks is usually long enough for them to be comfortable with concrete and a little bit of rocky ground for turnout, though not for riding. Depends on the horse though.
If he's miserable sore walking over those kinds of surfaces, I'd go ahead and shoe him, but if he's sore enough to be miserable I'd be concerned there's more going on than just not being shod. I wanted to add, 5 weeks is a long enough time to expect chipping in the barefoot horse. Mine have to be done every 3-4 weeks to prevent chipping, sometimes more, so he IS due for a farrier appointment, but I imagine it could wait until he got to your barn. You could also smooth the chips out with a regular hoof rasp or rider's rasp.
If getting a farrier is a big hassle and you're really concerned, some front hoof boots would do on a temporary basis. IMO, he'll be just fine as long as you aren't expecting to go charging down a gravel road with him.
Tug on anything at all and you'll find it connected to everything else in the universe.~John Muir