Introduction:
The question asks to find the number of 4 digit numbers greater than 5000 that can be formed using the digits 3,4,5,6,7 without any repetition.

Method:
To find the number of such numbers, we need to consider the following steps:

1. Count the total number of ways to choose 4 digits out of 5 without repetition.
2. Count the number of ways to choose 4 digits out of 5 such that the first digit is 5, and the remaining 3 digits can be any of the remaining 4 digits.
3. Count the number of ways to choose 4 digits out of 5 such that the first digit is 6 or 7, and the remaining 3 digits can be any of the remaining 4 digits.
4. Sum up the numbers obtained in steps 2 and 3 to get the total number of 4 digit numbers greater than 5000.

Solution:
1. Total number of ways to choose 4 digits out of 5 without repetition = 5P4 = 5x4x3x2 = 120.
2. Number of ways to choose 4 digits out of 5 such that the first digit is 5, and the remaining 3 digits can be any of the remaining 4 digits = 4P3 = 4x3x2 = 24.
3. Number of ways to choose 4 digits out of 5 such that the first digit is 6 or 7, and the remaining 3 digits can be any of the remaining 4 digits = (4P3)x2 = (4x3x2)x2 = 48.
4. Total number of 4 digit numbers greater than 5000 that can be formed = 24 + 48 = 72.

Conclusion:
Thus, the number of 4 digit numbers greater than 5000 that can be formed using the digits 3,4,5,6,7 without repetition is 72.