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The first digit can be any one of 1,2,3,4,5. With each choice of digit1, the second digit can be any one of 1,2,3,4,5 so making 5*5 two-digit numbers. With each of these, the third digit can be any one of 1,2,3,4,5 so making 5*5*5 three-digit numbers and so on.

The total number is 55 = 3125.

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