Let's call line : line k.
Find the equation of the line whose slope is the negative reciprocal of line K and it includes the point (5, 4). Call this line J. You will need to use the point-slope form equation:
Find the point of intersection of these 2 lines. The perpendicular distance from the pt 5, 4 to the line is the distance from (5,4) to the point of intersection.