The tire replacement in X-years that you read about are mostly for Class A motorhomes. ST "trailer tires" are not generally in that category of concern.
Assuming that your tires are in good shape, not driven too fast, not curb cut or other similar sidewall damage and most importantly both not over loaded and kept at max pressure listed on the side wall you are pretty safe.
Travel Trailer tires fail all the time - generally due to over heating due to overloading and under inflating. Trailer manufacturers use cheap tires to save money and are not always known for putting adequate or well made tires on their trailers. Though there are exceptions.
On a motorhome a front tire blowout can cause a massive wreck with loss of life - hence the very real concern with tire age on Class As. A blown tire on a TT is never fun and can cause body damage around the blowout but it doesn't lead to a wreck just a bad day changing a tire by the side of the road.
So, it's good to worry about your tires. But not all the much about their age. You may want to replace them with better tires (generally Goodyear brand ST tires are the gold standard) and even move up a load rating one or two levels - especially if your current tires are Load Rated "C" tires.
Be sure to keep an eye on your tire wear, make sure it's even - front to back and side to side. Keep them aired up to max cold psi before pulling out and watch for any telltale signs of problems with sidewall scuffs/cuts, etc.
Also, keep your axle bearings well packed and make sure your brakes are properly adjusted and working. These two things can effect the tires and their safety, too.
2017 Winnebago Adventurer 37F
2016 Lincoln MKX Toad