Since your original slope is - 4, you take the opposite reciprocal for the perpendicular line. This would be 1/4.
Now we have to solve for b in the slope-intercept form of y = mx + b. To find it, plug in the ordered pair given.
y = 1/4x + b
5 = 1/4(- 8) + b
5 = - 2 + b
5 + 2 = b
7 = b
Your equation is y = 1/4x + 7