The value of $$\frac{4}{5} \div 3\frac{1}{4}{\text{ of }}\frac{8}{{13}} - \frac{{\frac{1}{5} - \frac{1}{8}}}{{\frac{1}{5} + \frac{1}{8}}} \times 5\frac{1}{5} + \frac{5}{6}\,{\text{is:}}$$

$$\eqalign{ & \frac{4}{5} \div 3\frac{1}{4}{\text{ of }}\frac{8}{{13}} - \frac{{\frac{1}{5} - \frac{1}{8}}}{{\frac{1}{5} + \frac{1}{8}}} \times 5\frac{1}{5} + \frac{5}{6} \cr & = \frac{4}{5} \div \frac{{13}}{4} \times \frac{8}{{13}} - \frac{{\frac{1}{5} - \frac{1}{8}}}{{\frac{1}{5} + \frac{1}{8}}} \times 5\frac{1}{5} + \frac{5}{6} \cr & = \frac{2}{5} - \frac{3}{{13}} \times \frac{{26}}{5} + \frac{5}{6} \cr & = \frac{2}{5} - \frac{6}{5} + \frac{5}{6} \cr & = \frac{{12 - 36 + 25}}{{30}} \cr & = \frac{1}{{30}} \cr} $$