Find the slopes of each line to determine how they compare to each other. The slopes can be found using the form y1 - y2/x1 - x2, like so:
-7 - (-5)/-3 - (-7) => -7 + 5/-3 + 7 => -2/4 => -1/2 <---This is the slope of L1
-2 - (-6)/-5 - (-7) => -2 + 6/-5 + 7 => 4/2 => 2 <--- This is the slope of L2
Lines with slopes that are opposite reciprocals of each other are perpendicular, therefore these lines are perpendicular.