Explanation:
sin (theta) = - 5/13 in Q III
cos is also negative in Q III
then using sin^2 + cos^2 = 1 you will find cos = - 12/13
and tan = sin / cos = 5/12
adding π to theta just changes the signs of sin and cos (they will now both be positive) and tan will still be 5/12 (in Quadrant I)
5/12