5. The license plate numbers issued by a city consist of 6 digits (from 0 to 9), but it is required that any 2 license plates must have at least 2 different digits (for example, license plates 038471 and 030471 cannot be used simultaneously). Try to find the maximum number of different license plates that the city can issue. And prove it.
5. The answer is 100000. If 100001 license plates are issued, then by the pigeonhole principle, at least 10001 numbers will have the same first digit, and similarly, at least 1001 numbers will have the same second digit, $\cdots$, at least 2 numbers will have the same fifth digit, which would violate the rule. Using the following method, 100000 license plates can be issued while complying with the rule: the last 5 digits can be filled arbitrarily (there are $10^{5}$ ways to do this), and the first digit is filled with the unit digit of the sum of the last 5 digits, then if 2 numbers differ in only one of the last 5 digits, their first digit will also be different.