The units digit of a number is the digit located at the rightmost position. To find the units digit of 5745, we can simply look at the number itself and identify the digit in the units place.

Given number: 5745

Identifying the units digit:
The units digit of the given number is 5.

Therefore, the units digit of 5745 is 5.

Explanation:
To understand why the units digit of 5745 is 5, we need to look at the pattern of units digits for different powers of 5.

Pattern of units digits for powers of 5:
- 5^1 = 5
- 5^2 = 25
- 5^3 = 125
- 5^4 = 625
- 5^5 = 3125
- 5^6 = 15625

From the pattern, we can observe that the units digit of 5^1 is 5, the units digit of 5^2 is 5, the units digit of 5^3 is 5, and so on. This pattern repeats every 4 powers of 5.

Now, let's consider the units digit of 5745. We can express 5745 as a product of powers of 5:

5745 = 5^3 * 229

Since the units digit of 5^3 is 5, the units digit of 5745 will also be 5. This is because the units digit of any product is determined only by the units digits of the factors involved.

Therefore, the units digit of 5745 is 5.

Conclusion:
The units digit of the given number 5745 is 5. Hence, the correct answer is option D.