Let the required line be L
Slope of a line perpendicular to it is -x/y = -2/-5 = 2/5.
We Know that product of slopes of perpendicular lines is -1, So slope of line L is -5/2.
We know L passes through (0,-8)
y-(-8) = -5/2(x-0)
Therefore equation of line is 5x + 2y + 16 = 0