squeak-
Good puzzle.
The original number can end with either a 1 or a six (subtract 1, get a number divisible by 5)
the next four numbers must all end with 16, 36, 56, 76 or 96 (divisible by 4, subtract 1 divisibe by 5)
the last number must be 0 ot 5 (divisible by 5)
From that point on, brute force produces the following:
3121
2496
1996
1596
1276
1020