Because the balls and the boxes are both indistinguishable it is way simpler than it looks and the only way to this question is by listing all the possible cases.

Case 1: 4 balls in one box

Case 2: 3 balls in one box and 1 ball in a other box

Case 3: 2 balls in one box and 2 balls in a other box

Case 4: 2 balls in one box and 1 ball in a other box and 1 ball in a other box

Case 5: 1 ball in one box and 1 ball in a other box and 1 ball in a other box and 1 ball in a other box

Which shows that there are only **5** ways to distribute.