Introduction:
To find the number of 4-digit numbers without repetition of digits that are divisible by 5, we need to consider a few factors.

Step 1: Determine the range:
The range of 4-digit numbers is between 1000 and 9999 (inclusive).

Step 2: Identify divisible by 5:
To determine if a number is divisible by 5, we need to check if the last digit is either 0 or 5.

Step 3: Count the possibilities:
We will count the number of possibilities for each digit in the 4-digit number.

First Digit:
The first digit cannot be zero since it is a 4-digit number. So, there are 9 possibilities (1-9) for the first digit.

Second Digit:
The second digit can be any digit except the one used for the first digit. Since there are 9 possibilities for the first digit, there are 9 possibilities (0-9 excluding the first digit) for the second digit.

Third Digit:
The third digit can be any digit except the ones used for the first and second digits. So, there are 8 possibilities (0-9 excluding the first and second digits) for the third digit.

Fourth Digit:
To make the number divisible by 5, the last digit must be either 0 or 5. So, there are 2 possibilities for the fourth digit.

Calculating the Total:
To find the total number of 4-digit numbers without repetition that are divisible by 5, we multiply the number of possibilities for each digit.

Total = 9 (first digit) × 9 (second digit) × 8 (third digit) × 2 (fourth digit) = 1296

Therefore, there are 1296 4-digit numbers without repetition of digits that are divisible by 5.