Write the equation of a line that is perpendicular to the given line and that passes through given point -x+5y=14; (-5,-2) show your work

For perpendicular lines, m2 = -1/m1.

For line -x + 5y = 14 => 5y = x + 14 => y = 1/5 x + 14/5 => slope = 1/5

m2 = -1 / (1/5) = -5

Required equation is y - (-2) = -5(x - (-5))
y + 2 = -5(x + 5)
5x + y = -25 - 2
5x + y = -27