Find the Exact Value Under the Given Conditions Find $\tan ( \alpha - \beta ) .$

Multiple Choice

Find the exact value under the given conditions.
- $\cos \alpha = - \frac { 5 } { 13 } , \frac { \pi } { 2 } < \alpha < \pi ; \quad \sin \beta = \frac { 8 } { 17 } , \frac { \pi } { 2 } < \alpha < \pi \quad$ Find $\tan ( \alpha - \beta ) .$

A) $\frac { 50 } { 19 }$
B) $\frac { 20 } { 3 }$
C) $- \frac { 20 } { 3 }$
D) $- \frac { 140 } { 171 }$