Smallest 7 digit number that uses some (but not necessarily all) of the digits 0, 1, 2, 3, 5 and doesn't use any of the digits 4, 6, 7, 8, 9:
1237 * 819 = 1013103
Smallest 7 digit number that uses all of the digits 0, 1, 2, 3, 5 and doesn't use any of the digits 4, 6, 7, 8, 9:
1508 * 819 = 1235052
Smallest 7 digit number that uses all of the digits 0, 1, 2, 3, 5 and can use any of the digits 4, 6, 7, 8, 9:
1225 * 819 = 1003275