1. **State the problem:** We need to find the area of a circle with radius $r=5$ kilometers. 2. **Formula for the area of a circle:** $$A = \pi r^2$$ where $A$ is the area and $r$ is the radius. 3. **Substitute the given radius into the formula:** $$A = \pi \times 5^2$$ 4. **Calculate the square of the radius:** $$5^2 = 25$$ 5. **Multiply by $\pi$ to get the exact area:** $$A = 25\pi$$ 6. **Final answer:** The exact area of the circle is $$25\pi$$ square kilometers.