How far are you from your starting point when you walk $5\text{km}$ north and then turn $90^{\circ }$ to your left and walk another $5\text{km}$?

The paths walked form a right-angled triangle where:
* Vertical side (North path) $=5\text{km}$
* Horizontal side (West path after a $90^{\circ }$ left turn) $=5\text{km}$

The distance from the starting point to the final position is the hypotenuse ($d$) of this right-angled triangle. Applying Pythagoras' theorem:

$$d=\sqrt{5^2+5^2}$$

$$d=\sqrt{25+25}=\sqrt{50}$$

$$d=5\sqrt{2}\approx 5\times 1.414=7.07\text{km}$$

Rounding to the nearest integer option gives $7\text{km}$.