Модуль: Amount of information. Probabilistic approach

Задача

Veselchak U invented a password generator that generates passwords 5 characters long. Each character is taken with equal probability from a set containing X characters. It is known that the message "your password is a palindrome" carries in itself exactly 10 bits of information less than the message "the next password consists of the same characters". It is also known that when calculating the amount of information in each of these messages, immediately, without rounding, an integer number of bits was obtained. Determine the number of X characters for which this ratio will be valid.

We will consider a palindrome such a sequence of characters that will be read the same way from left to right and right to left, for example ABCBA or BBBBB.
Please answer with a whole number.