Given sin $\displaystyle \theta$ = $\displaystyle \frac{-5}{13}$ in quadrant III, tan $\displaystyle \phi$ = $\displaystyle \frac{-8}{15}$ in quadrant II; find the value of sin($\displaystyle \theta$ + $\displaystyle \phi$):

I've posted my solution -- which the answer key says is wrong -- here, http://imagebin.ca/img/tnINM0J.png .

Please tell me what I'm doing wrong.