1. **State the problem:** Find the equation of a line in slope-intercept form $y=mx+b$ that passes through the point $(5,5)$ with slope $m=-\frac{5}{6}$. 2. **Recall the slope-intercept form:** The equation is $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept. 3. **Use the point-slope form to find $b$:** Substitute $x=5$, $y=5$, and $m=-\frac{5}{6}$ into $y=mx+b$: $$5 = -\frac{5}{6} \times 5 + b$$ 4. **Calculate the product:** $$5 = -\frac{25}{6} + b$$ 5. **Solve for $b$:** $$b = 5 + \frac{25}{6} = \frac{30}{6} + \frac{25}{6} = \frac{55}{6}$$ 6. **Write the final equation:** $$y = -\frac{5}{6}x + \frac{55}{6}$$ 7. **Check the options:** None of the options exactly match this equation, so the correct slope-intercept form is $y = -\frac{5}{6}x + \frac{55}{6}$, which is not listed among A, B, C, or D. **Final answer:** $$y = -\frac{5}{6}x + \frac{55}{6}$$