the equation of line L1 is 2y-5x-8=0 and line L2 passes through the points (-5,0) and(5,-4). show that the two lines are perpendicular
If they are perpendicular, you know that their slopes must be negative reciprocals of each other.
You also know that the slope of L1 is 5/2.
Show the slope for L2 is -2/5.