1. **State the problem:** Find the area of the shaded sector of a circle where the central angle $m\angle WOX = 60^\circ$ and the radius is 5 ft. 2. **Formula for the area of a sector:** $$A = \frac{\theta}{360^\circ} \times \pi r^2$$ where $\theta$ is the central angle in degrees and $r$ is the radius. 3. **Substitute the given values:** $$A = \frac{60}{360} \times \pi \times 5^2$$ 4. **Simplify the fraction:** $$A = \frac{60}{360} \times \pi \times 25 = \frac{1}{6} \times 25\pi$$ 5. **Final area:** $$A = \frac{25\pi}{6}$$ The correct answer is **C. $\frac{25\pi}{6}$**.