It's 3-5 days FROM THE TIME OF PICK UP.
So just because someone prints a label and you get an email with a tracking number, the 3-5 day countdown does not start yet.
If I print a priority label at 3pm and then go drop the package in the blue mailbox, the mailbox says pickup time is 2:15pm each day. Since I've already missed today's pickup, it really does not get moving until a full day later.
If I'm lazy and don't put it into the mailbox until tomorrow after work, I have added 2 days to the shipping time.
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I normally can Priority a package from Cinci to Hollywood in 2 day flat - if I can get it to the mailbox before 2:15pm.