6.4. A five-digit number is a multiple of 54, and none of its digits are 0. After deleting one of its digits, the resulting four-digit number is still a multiple of 54; after deleting one of the digits of this four-digit number, the resulting three-digit number is still a multiple of 54; after deleting one of the digits of this three-digit number, the resulting two-digit number is still a multiple of 54. Find the original five-digit number.
6.4. The original five-digit number is 59994.

Since the number faced after each deletion of the front or back is a multiple of 9, the number deleted each time is a multiple of 9. This means that only a 9 can be deleted each time, and the last remaining two-digit number can only be 54. Among the three-digit numbers 549, 594, 954, only 594 is a multiple of 54. Therefore, the three-digit number obtained after two deletions is 594. Among the four-digit numbers 9594, 5994, 5949, only 5994 is a multiple of 54, so the four-digit number obtained after the first deletion is 5994. Finally, among the five-digit numbers 95994, 59994, 59949, only 59994 is a multiple of 54.