A man walks $5\text{ km}$ North, then turns right and walks $3\text{ km}$. Then he turns right again and walks $5\text{ km}$ and makes a U-turn. Which direction is he facing now?

Let's trace the direction changes step by step:
1. Starts walking North $\to$ Facing North.
2. Turns right $\to$ Facing East.
3. Turns right again $\to$ Facing South. He walks $5\text{ km}$ in this direction.
4. Makes a U-turn $\to$ A U-turn completely reverses the current facing direction.

$$\text{Opposite of South}=\text{North}$$

Therefore, he is facing North now.