5. Determine an equation for the perpendicular (right) bisector of the line segment with endpoints $D(-3,5)$ and $M(7,-9)$.

Step 1 ：Find the midpoint of the line segment DM: \(M = \left(\frac{-3+7}{2}, \frac{5-9}{2}\right) = (2, -2)\)

Step 2 ：Find the slope of the line DM: \(m = \frac{-9-5}{7-(-3)} = \frac{-14}{10} = -\frac{7}{5}\)

Step 3 ：Find the negative reciprocal of the slope: \(m_{perp} = \frac{5}{7}\)

Step 4 ：Use the point-slope form to find the equation of the perpendicular bisector: \(y + 2 = \frac{5}{7}(x - 2)\)

Step 5 ：\boxed{y + 2 = \frac{5}{7}(x - 2)}