Mahtematical and statistical reasoning makes it evident that there is a mistake in the writing of the question and the digits were duplicated. So the right question is:
"You need to have a password with 5 letters followed by 3 odd digits between 0 and 9, inclusive. If the characters and digits cannot be used more than once, how many choices do you have for your passwor?"
The solution is:
5 letters from 26 with no repetition => 26*25*24*23*22 different choices.
odd digits are 1, 3, 5, 7 and 9 => 5 different digits to choose
3 digits from 5 with no repetition => 5*4*3 = 60
Then, the total number of choices is: 26*25*24*23*22*60 = 473,616,000
