1. **State the problem:** Given a slope (pitch) of $\frac{5}{12}$ and a run (horizontal distance) of 10, find the rise (vertical height). 2. **Recall the formula for slope:** $$\text{slope} = \frac{\text{rise}}{\text{run}}$$ 3. **Substitute the known values:** $$\frac{5}{12} = \frac{\text{rise}}{10}$$ 4. **Solve for rise by multiplying both sides by 10:** $$\text{rise} = 10 \times \frac{5}{12}$$ 5. **Simplify the multiplication:** $$\text{rise} = \frac{10 \times 5}{12} = \frac{50}{12}$$ 6. **Simplify the fraction by dividing numerator and denominator by 2:** $$\text{rise} = \frac{\cancel{50}^{{25}}}{\cancel{12}^6} = \frac{25}{6}$$ 7. **Convert to decimal for easier interpretation:** $$\frac{25}{6} \approx 4.17$$ **Final answer:** The rise is $\frac{25}{6}$ or approximately 4.17 units.