Note:

1) The 5 digits must be different

2) The 1st, 2nd, 3rd and 4th digits cannot be 1, because 1 divides the sum of the 5 digits.

3) The first digit must be a multiple of the 2nd digit

The only possibility for the first two digits are therefore

42

62

82

93

84

4) The third digit must divide the sum of the first two, but it cannot be a multiple of the 2nd digit.

4 + 2 = 6, which makes 423 a possibility for the 1st 3 digits

6 + 2 = 8, so nothing works as a 3rd digit

8 + 2 = 10, which makes 825 a possibility

9 + 3 = 12, which makes both 932 and 934 possibilities

8 + 4 = 12, which makes 843 **and 846** a possibility

recapping, the first 3 digits must be

423

825

932

934

843 or

**846**

5) The 4th digit must divide the sum of the first three. but it cannot be a multiple of any of the first 3

4+2+3 = 9, so nothing works as a 4th digit

8+2+5 = 15, but 3 cannot be the 4th digit, because 2 divides 18