F5 E2 and F05 E02 indicate that the front-load Brastemp BNF15 is not confirming the door lock. They should not be reduced to any F5 code or transferred to a top-load lid.
The definition is documented in the BNF15ASANA manual. The check starts with the visible latch, not by replacing the lock.
Check whether something is preventing it from seating
Cancel or pause according to the manual and wait for the drum to stop and for the door to be able to open. Move away any clothing that is sticking out and check whether the laundry is pressing from inside. Look for damage to the latch and close it without slamming or holding force.
If there is already water inside or the unit is still hot, do not pull on the handle to repeat the check. A closed door does not guarantee that the control has received the lock confirmation.
If the alert returns with the perimeter clear, request a check of the locking system. The door lock check and opening and closing problems cover the related situations. Do not make electrical jumpers or use internal releases from another platform.
Note whether F5 E2 appears before filling or when resuming an interrupted cycle; that helps identify the lack of confirmation.