1. **State the problem:** A man walks 5 km east and then 12 km north. We need to find his displacement, which is the straight-line distance from his starting point to his final position. 2. **Visualize the problem:** The man's path forms a right triangle where the legs are 5 km (east) and 12 km (north). 3. **Apply the Pythagorean theorem:** The displacement $d$ is the hypotenuse of the right triangle. $$d = \sqrt{5^2 + 12^2}$$ 4. **Calculate:** $$d = \sqrt{25 + 144} = \sqrt{169} = 13$$ 5. **Interpretation:** The man's displacement is 13 km in a straight line from his starting point. **Final answer:** The displacement is $13$ km.