Let \( S \) be the set of all passwords which are six to eight characters long, where each character is either an alphabet from \( \{A,B,C,D,E\} \) or a number from \( \{1,2,3,4,5\} \) with the repetition of characters allowed. If the number of passwords in \( S \) whose at least one character is a number from \( \{1,2,3,4,5\} \) is \( \alpha \times 5^{6} \), then \( \alpha \) is equal to ________.
