I don't have a Student Prince schematic but this bit from the Cabaret schematic might be similar:
Cabaret Game Over relay (resized).jpg
In a 3 ball game the blue-brown wire on the Ball Count Unit is shorted to the blue-red wire (as shown) that leads to the Game Over trip relay. In a 5 ball game there should be no connection between those two wires. The blue-brown wire might be getting shorted to the blue-red on a 5 ball game when the Ball Count Unit reaches the 4th ball. Check those two wires both at the Ball Count Unit and at the 3/5 ball adjustment dial.

/Mark