X travels $5\text{km}$ north, turns right and covers $7\text{km}$. He then turns right and travels $5\text{km}$. In which direction is he going?

Let's map the sequential turnings:
1. Facing North initially.
2. Turns Right $\to$ facing East.
3. Turns Right again $\to$ facing South.
Therefore, he is currently moving in the South direction.