Aman drives $5\text{km}$ from point A towards the south. He then takes a left turn and drives $5\text{km}$. He then takes a right turn and drives $5\text{km}$. He again takes a right turn and drives $10\text{km}$. He finally takes a right turn and drives $10\text{km}$ to reach point B. How much and in which direction does he have to drive to return to point A? (All the turns are $90^{\circ }$ turns only.)

Let's trace Aman's movement path using a coordinate system, setting starting point A at $(0,0)$:
1. **From A $(0,0)$ **, drives $5\text{km}$ South $\to$ reaches $(0,-5)$.
2. Turns left (faces East), drives $5\text{km}$ $\to$ reaches $(5,-5)$.
3. Turns right (faces South), drives $5\text{km}$ $\to$ reaches $(5,-10)$.
4. Turns right (faces West), drives $10\text{km}$ $\to$ new X-coordinate $=5-10=-5$. Reaches $(-5,-10)$.
5. Finally turns right (faces North), drives $10\text{km}$ $\to$ new Y-coordinate $=-10+10=0$. Reaches point B at $(-5,0)$.

To return from point B $(-5,0)$ to starting point A $(0,0)$:

* Horizontal distance $=0-(-5)=5\text{km}$.
* Since point A is to the right of point B along the X-axis, Aman must drive towards the East.

Therefore, he needs to drive $5\text{km}$ towards the east.