If you observe carefully, when we stack paper cups on top of others, you will realise that a section of the paper cups can be seen. Let this small section be 1 unit.

Removing 5 cups means removing 5 of these away, so 5 units of height has been removed.

Clearly the 5 cups removed also results in a height drop of 46 - 38.5 = 7.5 cm.

So, 5 units = 7.5 cm
1 unit = 1.5 cm

So 1,5 cm of each cup can be seen (except for the bottom one in which the full 13 cm can be seen).

Look at the version with 4 paper cups. There are 3 cups in which 1.5 cm can be seen and 1 bottom cup in which the full 13 cm can be seen.

Height of wooden box
= 38.5 - 1.5 - 1.5 - 1.5 - 13
= 21 cm