To form a 5-digit number that does not contain the digits 0 or 8, you have 8 choices for each digit (1, 2, 3, 4, 5, 6, 7, and 9), because you can't use 0 or 8. Since you're choosing from 8 different options for each of the 5 digits, you can calculate the total number of such 5-digit numbers as:
8 choices * 8 choices * 8 choices * 8 choices * 8 choices = 8^5 = 32,768
So, there are 32,768 different 5-digit numbers that can be formed without using the digits 0 or 8.