1. **State the problem:** We need to find the slope of a line parallel to the line given by the equation $$y = -\frac{5}{8}x + 5$$ and the slope of a line perpendicular to this line. 2. **Recall the slope form:** The equation is in slope-intercept form $$y = mx + b$$ where $$m$$ is the slope. 3. **Identify the slope of the given line:** From $$y = -\frac{5}{8}x + 5$$, the slope $$m = -\frac{5}{8}$$. 4. **Slope of a parallel line:** Parallel lines have the **same slope**. So, the slope of a line parallel to the given line is $$-\frac{5}{8}$$. 5. **Slope of a perpendicular line:** The slope of a line perpendicular to another is the **negative reciprocal** of the original slope. Calculate the negative reciprocal: $$m_{\perp} = -\frac{1}{m} = -\frac{1}{-\frac{5}{8}} = -\cancel{1} \times \frac{8}{\cancel{5}} = \frac{8}{5}$$ 6. **Final answers:** - Slope of parallel line: $$-\frac{5}{8}$$ - Slope of perpendicular line: $$\frac{8}{5}$$