1. **State the problem:** Solve the equation $5x - 4y = 5$ for $y$ and express it in slope-intercept form $y = mx + b$. 2. **Rewrite the equation:** Start with the given equation: $$5x - 4y = 5$$ 3. **Isolate the $y$ term:** Subtract $5x$ from both sides: $$-4y = -5x + 5$$ 4. **Divide both sides by $-4$ to solve for $y$:** $$y = \frac{-5x + 5}{-4}$$ 5. **Simplify the fraction:** $$y = \frac{-5x}{-4} + \frac{5}{-4} = \frac{5}{4}x - \frac{5}{4}$$ 6. **Interpret the result:** The equation in slope-intercept form is: $$y = \frac{5}{4}x - \frac{5}{4}$$ This means the slope $m$ is $\frac{5}{4}$ and the y-intercept $b$ is $-\frac{5}{4}$. **Final answer:** $$y = \frac{5}{4}x - \frac{5}{4}$$