The length of the rectangle is the distance between the points (-5, 2) and (-5, -4), which is 6 units. The width of the rectangle is the distance between the points (-5, 2) and (4, 2), which is 9 units. The area of the rectangle is length times width, which is 6 times 9, or 54 square units.
Therefore, the area of the rectangle is 54 square units.