Final answer:
The numbers greater than 5000 that can be formed using the digits 1, 2, 3, 4, and 5 without repeating any digit is 120.
Step-by-step explanation:
The numbers greater than 5000 that can be formed using the digits 1, 2, 3, 4, and 5 without repeating any digit can be found by considering the different positions of the digits.
Step 1: Choose the first digit. There are 5 options for the first digit since we can choose any of the 5 digits. (5 options)
Step 2: Choose the second digit. There are 4 options for the second digit since we cannot repeat the digit used in the first step. (4 options)
Step 3: Choose the third digit. There are 3 options for the third digit since we cannot repeat the digit used in the first two steps. (3 options)
Step 4: Choose the fourth digit. There are 2 options for the fourth digit since we cannot repeat the digit used in the first three steps. (2 options)
Step 5: Choose the fifth digit. There is 1 option for the fifth digit since we cannot repeat the digit used in the first four steps. (1 option)
By multiplying the number of options at each step, we can find the total number of numbers greater than 5000 that can be formed: 5 x 4 x 3 x 2 x 1 = 120.