The slope of a line perpendicular to a given line will always have a slope that is the opposite reciprocal. This means that whatever the original slope is, the slope of the perpendicular line will have the opposite sign and is the flipped fraction.
For example, the slope of a line perpendicular to a line with a slope of 2 would be -1/2
In this case, the slope is -4/5, so the slope of the perpendicular line would have the opposite sign, +, and is flipped, 5/4.
Therefore, the answer is a slope of 5/4, or answer choice A