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