According to https://www.computerbase.de/artikel/grafikkarten/nvidia-geforce-rtx-5060-ti-16-gb-test.92119/seite-8#abschnitt_leistungsaufnahme_gaming_die_lastspitzen it peaks at 201 W.
As others mentioned, the rest of the PC is important too, but there's also differences in PSU quality. IIRC ATX 3.x requires them to actually be able to supply the nominal power continuously, with short spikes up to twice that. While older and cheaper PSUs often listed the peak output which they couldn't sustain, that's why a lot of power supply calculators recommend a much higher wattage than strictly necessary.
So, assuming a "65 W" AMD CPU which maxes out at 88 W plus the 200 W GPU plus a 50 W buffer for mainboard and drives etc., a good new 350 W PSU should run such a system (assuming you could actually buy one, the lowest ATX 3.x PSUs I've seen start at 450 W).
But to answer the question if you can continue to use your old PSU you a) need to know how much the rest of the system needs, mainly the CPU (which as others have mentioned can range from under 100 W to ~300 W), and b) the real power your PSU can supply which depends on its age and quality - maybe tell us the exact CPU and PSU in question.
Slowing cell aging could mean better health for longer, even if you don't die (much) later.