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Answer:
900
Step-by-step explanation:
None of the numbers beginning with 8 are palindromic. There aren't very many numbers that are that are also 5 digits long.
The first digit cannot be 0 (otherwise you will wind up with a 4 digit number)
The first digit can be 9 others.
The second digit can be all 10 digits
The third digit can also be all 10 digits.
The first digit and the 5th digit must be the same so the fifth digit does not add anything new or more palindromic numbers.
The 2nd and 4th must also be the same.
So the total number of palindromic numbers that are 5 digits long
9 * 10 * 10 = 900
There really aren't any more.
80908 is one example of a palindromic 5 digit number.