Find $\displaystyle {\tan{{\left(\alpha-\beta\right)}}}$ exactly, given $\displaystyle {\sin{\alpha}}=-\frac{{5}}{{8}}$  and $\displaystyle {\cos{\beta}}=-\frac{{3}}{{4}}$ where $\displaystyle \alpha$ terminates in quadrant III and $\displaystyle \beta$ terminates in quadrant II. Be sure to reduce your final result completely.