1. **State the problem:** Find the volume of a cone with height $12$ yards and base radius $5$ yards. 2. **Formula:** The volume $V$ of a cone is given by the formula: $$V = \frac{1}{3} \pi r^2 h$$ where $r$ is the radius of the base and $h$ is the height. 3. **Substitute values:** Here, $r = 5$ yd and $h = 12$ yd. $$V = \frac{1}{3} \pi (5)^2 (12)$$ 4. **Calculate:** $$V = \frac{1}{3} \pi \times 25 \times 12$$ $$V = \frac{1}{3} \pi \times 300$$ 5. **Simplify:** $$V = 100 \pi$$ 6. **Final answer:** The volume of the cone is $$\boxed{100 \pi \text{ cubic yards}}$$ This means the cone holds $100 \pi$ cubic yards of space, which is approximately $314.16$ cubic yards when using $\pi \approx 3.1416$.