No, Kelly, you shouldn’t need to worry about that quite yet. Yes, you’ll hear different numbers from different people, and the same will undoubtedly occur here in response to your question. But the commonly accepted one is six to seven years, and they are too expensive to switch out before necessary. My original Goodyear’s were 9 when we replaced them with Toyos, and were like yours in great condition. They spent 95% of their life fully shaded from sun, though, unlike most. Motor home tires age out before they wear out, and between years 7 and 9 I fretted a bit until we could afford new ones.
A better current investment would be chassis improvements like a steering stabilizer if the coach doesn’t already have one. There is peace of mind in a Safe-T-Plus, for example, that can assist handling in the event of a failure regardless of brand new or 9 year-old tires. The bonus is improved handling in wind, uneven roads, and passing trucks.
Joel