The OP is flying T3 to T5, not the other way around. From what I remember, T5 does not have TSA pre, but has a premium security line for elites. In any case, this can go either way. I would be nervous because the long flight is second, so in any mishaps you would need to be rebooked for the long haul flight, which means you could lose your good/premium seats, or invalidate any of your Covid tests.