The answer to this question is 10,156,250. There are 26 choices for the first letter. Once the first letter is chosen, there are 25 options for the second letter, then 25 options for the third letter (cannot take the second but can take any other letter), then 25 choices for the fourth letter (cannot take the third), then 25 choices for the fifth letter (cannot take the fourth). Therefore, there are 26⋅25^4 = 10,156,250 such five-letter words.