Of course, there is still hope that a repair might be possible.
"However, both I and the car are currently abroad, and it's unfortunately not possible to simply open the transmission and take a look. I don't need the car here, but I will need it in Germany. Therefore, the repair time should be as short as possible."
Is the current gearbox repairable, or specifically the 5th gear? If so, we will definitely do that. However, if it's not possible to fix it, we would need a different gearbox. That's why I'm already searching for a suitable one. Now we can take our time and search without being under pressure

. Therefore, I'm also asking what alternatives are available...