tire size for 5th wheel

Crawl under it and look at the axle tag, with 5 lug wheels most likely a 3500lb axle. If it were mine I'd want the ST225/75/R15C at a minimum. Might as well get the D range tires.

Do you know what the current axles and wheels are rated for? What the trailer GVWR is? What's on it now is not satisfactory IMO and will result in unwanted misery at some point.

My old 5er had ST205/75/R15s load range c tires on it when I bought it. When I was time for news tires I went with ST225/75/R15 LR E. They had a much higher weight buffer which gave me a lot of peace of mind.

Welcome to the Forum.
At 1260# max load, those tires are only 50# above your trailers DRY weight (and this assumes 20% on the pin).
Previous owner is correct - you need higher capacity tires.
Look at the GVWR/Tire pressure label towards the front left side of the trailer.
What is the OEM tire size, load rating and pressure displayed on there?
THAT is your minimum starting point.
Most on here, including me, recommend bumping the tires up at least one load range to buy a little more safety margin.

I would add you don't want a P tire but a ST /LT or a all position tire is required for the trailer that size. P (passenger) work ok on small light weight trailers.

If those 1260 lb rated tires are a P tire their load capacity is actually reduced by dividing 1.1 = 1145 lbs per fed regulations.

Anyhow.....not knowing how much tire you actually need lets say that 2750 kg dry weight may be 6050 lbs. The GVWR may be closer to 7000-7500 lbs which figures around 1875 lbs per tire.

That fits nicely with the ST205/75-15 C at 1820 lbs per tire at the minimum. Or a good upgrade from the ST is the Vanco 2 commercial grade all position tire from Continental tire.

Actual tire size and load rating depend on the trailers GVWR in your case.

What is the trailers GVWR? Your axles will be rated to carry 80% of the trailers GVWR. Tires should be rated to equalmor exceed your axle rating.

Oh boy, here we go.

You want trailer tires not passenger car tires. The trailer tires have a heavier sidewall. You might want to check tirerack.com and see what they offer in that size for trailer tires. They show the weight a tire can support. You don't have to buy there but you can gather info.