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