Say that a positive integer is “five-important” if it is a multiple of 5 and/or contains the digit 5. For instance, the numbers 55, 120, and 456 are five-important, but the number 2019 is not. Say that a number is “super-five-important” if it is five-important and remains five-important after erasing any one of its digits. For instance, the numbers 5070, 5005, and 5577 are super-five-important, but the numbers 5, 100, 2019, and 2015 are not. How many different super-five-important numbers are there between 1 and 2019?
