Dennis, I'm SURE the OEM wheels that came on your trailer WERE 15" ones! Yes, I'd get 15" wheels and tires to match. In fact, I believe the OEM tires should be 205/75-R15, but your sticker would show what yours should be. I suspect it came with Load Range C tires, but I'd try to find Load Range D ones if you can. Maxxis makes this tire and the new Goodyear Endurance is also available in this Load Range. The Goodyears have a higher speed rating too.
Hi-Lo 1707T - Tire Minder TPMS on Tow Vehicle and Trailer, 300W Solar Battery Charger, Equal-i-zer WDH
2014 F150 Platinum 4x4 3.5L EcoBoost SCrew