1. **State the problem:** We have a circle with diameter 14 ft and an inscribed rectangle inside it with length 13 ft and height 5 ft. We want to find the area of the shaded region, which is the area of the circle outside the rectangle. 2. **Formula for the area of a circle:** $$\text{Area}_{circle} = \pi r^2$$ where $r$ is the radius of the circle. 3. **Calculate the radius of the circle:** Since the diameter is 14 ft, $$r = \frac{14}{2} = 7 \text{ ft}$$ 4. **Calculate the area of the circle:** $$\text{Area}_{circle} = \pi \times 7^2 = 49\pi$$ 5. **Calculate the area of the rectangle:** $$\text{Area}_{rectangle} = \text{length} \times \text{height} = 13 \times 5 = 65$$ 6. **Calculate the shaded area (area outside the rectangle but inside the circle):** $$\text{Area}_{shaded} = \text{Area}_{circle} - \text{Area}_{rectangle} = 49\pi - 65$$ 7. **Final answer:** The area of the shaded region is $$49\pi - 65 \text{ square feet}$$