Final answer:
The number of distinct 5-letter passwords without letter repetition can be found using the permutation calculation, which is 26×25×24×23×22.
Step-by-step explanation:
The number of distinct 5-letter (lowercase) passwords possible without repetition can be calculated by using the permutation formula, which considers the order and the fact that no letters can be repeated. In this case, the first position can be filled by any of the 26 letters of the alphabet, the second position can be filled by the remaining 25 letters, and so on until the fifth position, which can be filled by 22 letters.
Therefore, the calculation is 26×25×24×23×22.