Question Analysis:
In this question, a man is described as walking in different directions. We need to determine the final direction he is facing from the starting point. Let's analyze the given information step by step.

Given Information:
- The man walks 5 km towards the south.
- Then, he turns to the right and walks 3 km.
- After that, he turns to the left and walks 4 km.
- Finally, he goes back 10 km straight.

Solution:
To determine the final direction of the man, we need to analyze each step of his movement and find the net displacement.

Step 1: Walking 5 km towards the south
When the man walks 5 km towards the south, we can represent this as a movement in the "South" direction. The net displacement after this step is 5 km South.

Step 2: Turning right and walking 3 km
After walking 5 km towards the south, the man turns right and walks 3 km. Turning right from the south direction means he is now facing west. Therefore, this step can be represented as a movement in the "West" direction. The net displacement after this step is 3 km West.

Step 3: Turning left and walking 4 km
Next, the man turns left from the west direction and walks 4 km. Turning left from the west direction means he is now facing south. Therefore, this step can be represented as a movement in the "South" direction. The net displacement after this step is 4 km South.

Step 4: Going back 10 km straight
Finally, the man goes back 10 km straight. Going back in the opposite direction means he is moving in the opposite direction of his current facing. Since his current facing is south, he will move in the opposite direction, which is north. Therefore, this step can be represented as a movement in the "North" direction. The net displacement after this step is 10 km North.

Final Direction:
To determine the final direction, we need to find the net displacement after all the steps. The net displacement is obtained by adding the individual displacements in the x and y directions.

In this case, the net displacement in the x direction is 3 km West - 10 km North = -7 km West.
The net displacement in the y direction is 5 km South + 4 km South = 9 km South.

Since the net displacement in the x direction is negative and the net displacement in the y direction is positive, the man is facing towards the North-West direction from the starting place.

Therefore, the correct answer is option 'B' - North-West.