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 of a line 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:** $$5=\frac{25}{6} + b$$ 5. **Solve for $b$:** $$b=5 - \frac{25}{6} = \frac{30}{6} - \frac{25}{6} = \frac{5}{6}$$ 6. **Write the final equation:** $$y=\frac{5}{6}x + \frac{5}{6}$$ 7. **Check options:** The correct choice is A or B (both are the same): $y=\frac{5}{6}x + \frac{5}{6}$.