1. **State the problem:** Rewrite the equation $5x - 5y = -17$ in slope-intercept form, which is $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept. 2. **Start with the given equation:** $$5x - 5y = -17$$ 3. **Isolate the $y$-term:** Subtract $5x$ from both sides: $$-5y = -5x - 17$$ 4. **Divide both sides by $-5$ to solve for $y$:** $$y = \frac{-5x - 17}{-5}$$ 5. **Simplify the fraction by dividing each term separately:** $$y = \frac{-5x}{-5} + \frac{-17}{-5}$$ 6. **Cancel common factors:** $$y = \cancel{\frac{-5}{-5}}x + \frac{17}{5}$$ 7. **Simplify the coefficients:** $$y = 1x + \frac{17}{5}$$ 8. **Write the final slope-intercept form:** $$y = x + \frac{17}{5}$$ This means the slope $m$ is $1$ and the y-intercept $b$ is $\frac{17}{5}$. **Final answer:** $$y = x + \frac{17}{5}$$