15" trailer wheels can come in 5 or 6 lug hubs. If you have 6 lug wheel your part way there.
I doubt you can find a 5 lug 16" trailer wheel. Trailer wheel need to have a zero off set.
My old 1997 11200 lb 5th wheel trailer came with 5200 lb axles/6 lugs and 15" ST225/75-15 D Marathons. Sold wheels/tires to a guy with a lawn service trailer.
I bought four 16" grey steel modular trailer wheels (1997) from my local commercial trailer mfg. I thought I had wheel well clearance issues so went to a LT225/75-16 E at 2680 lbs. Next sets have been a bit taller in a LT215/85-16 E at 2680 lbs. Run all my LT E tires on rv and non rv trailers at max 80 psi.
The taller (32" dia) LT235/85-16 E at 3042 lbs capacity works better on heavier trailers with loaded 5.2k...6k axles.
LT tires that their mfg has recommended to me for my trailer use are;;
Cooper Discoverer HT-3
Bridgestone R-238 all steel ply carcass commercial grade
Michelin XPS Rib commercial grade all steel ply carcass
Goodyear Wrangler HT
BFG Commercial A/T 2
Firestone Transforce HT
Be sure and make your wheel well measurements first for proper clearance issues.