If cos theta is -5/13 and sin θ < 0, what is tan θ ?

Take the right angled triangle  with sides 13, 12 and 5. sine theta will be 12/13

When sin theta < 0 and cos theta < 0  we are in the  third  quadrant  so sin theta will be -12/13

tan theta = sin theta / cos theta  = -5/13 /  -12/13   = -5*13 / -12*13 =  5/12
 

(6,0) i hope it makes enough sense