Let us first find the angle adjacent to θ. To find this we can construct a right triangle by drawing a line segment from the point (-12,5) straight down to the x-axis. Using right triangle trig...
tan(adjacent angle)=5/12
adjacent angle=22.62 degrees
Since the two angles make a linear pair.
θ=180-22.62=157.38 degrees
cos(157.38 degrees) = -0.92
answer: -0.92