1. **State the problem:** Find the surface area of a cylinder with height $h=5$ km and radius $r=7$ km. 2. **Formula for surface area of a cylinder:** $$\text{Surface Area} = 2\pi r^2 + 2\pi rh$$ This formula includes the areas of the two circular bases ($2\pi r^2$) and the rectangular side wrapped around the cylinder ($2\pi rh$). 3. **Substitute the given values:** $$2\pi (7)^2 + 2\pi (7)(5)$$ 4. **Calculate each term:** $$2\pi \times 49 + 2\pi \times 35$$ 5. **Simplify:** $$98\pi + 70\pi = 168\pi$$ 6. **Calculate numerical value:** $$168 \times 3.1416 \approx 527.787$$ 7. **Round to the nearest thousandth:** $$527.787$$ **Final answer:** The surface area of the cylinder is approximately $527.787$ square kilometers.