because the process

is fully reversible --- i.e., if 1 top vertex is reached, then there is one and only one path (following the same rules) to go back to the starting point. Therefore, no two monkeys will reach the same top (otherwise, they would have to start from the same bottom).
However, there are only finite number of ropes, therefore, after finite steps, every monkey must reach top nodes. Therefore, all 5 top nodes must be reached.
QED