Hi,

Try to list them in an orderly fashion. First of all what if all 5 digits are 5? There is only one item,

55555.

Next, what if exactly 4 of the digits are 5? The remaining digit is a 2 and it can go in any of the 5 positions so there are 5 items with exactly 4 of the digits being 5.

25555
52555
55255
55525
55552.

What if exactly 3 of the digits are 5? That would mean that exactly 2 of the digits are 2. Suppose the leftmost 2 is in the first position. Where could the other 2 go?

22555
25255
25525
25552.

Suppose the leftmost 2 is in the second position. Where could the other 2 go?

Can you complete the list?

Penny