Student or Learner
Is my sentence correct?
The cashier opened the cash register (till) to sort out the coins.
"to sort" means to arrange the things that are there.
If the cashier is going to group the coins worth 25 cents with the other coins worth 25 cents, the coins worth 10 cents with the other coins worth 10 cents, that's sorting.
(Most cash drawers would keep these coins in separate compartments, and also separate from the paper money, so it's unlikely the cashier would need to either sort OUT the coins or sort the coins.)
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.