1. **State the problem:** Find the equation of a line with slope $m=\frac{5}{4}$ that passes through the point $(-8,3)$.\n\n2. **Formula used:** The point-slope form of a line is given by $$y - y_1 = m(x - x_1)$$ where $(x_1,y_1)$ is a point on the line and $m$ is the slope.\n\n3. **Substitute known values:** Here, $m=\frac{5}{4}$, $x_1=-8$, and $y_1=3$. So, $$y - 3 = \frac{5}{4}(x - (-8)) = \frac{5}{4}(x + 8)$$\n\n4. **Simplify the equation:** Distribute the slope on the right side: $$y - 3 = \frac{5}{4}x + \frac{5}{4} \times 8 = \frac{5}{4}x + 10$$\n\n5. **Solve for $y$ to get slope-intercept form:** $$y = \frac{5}{4}x + 10 + 3 = \frac{5}{4}x + 13$$\n\n**Final answer:** The equation of the line is $$y = \frac{5}{4}x + 13$$.