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

$$\frac{4}{5}\div3\frac{1}{4}$$ of $$\frac{8}{13}-\frac{\frac{1}{5}-\frac{1}{8}}{\frac{1}{5}+\frac{1}{8}}\times5\frac{1}{5}+\frac{5}{6}=\frac{4}{5}\div\frac{13}{4}$$ of $$\frac{8}{13}-\frac{\frac{3}{40}}{\frac{13}{40}}\times5\frac{1}{5}+\frac{5}{6}$$

$$=\frac{4}{5}\div2-\frac{3}{13}\times\frac{26}{5}+\frac{5}{6}$$

$$=\frac{2}{5}-\frac{3}{13}\times\frac{26}{5}+\frac{5}{6}$$

$$=\frac{2}{5}-\frac{6}{5}+\frac{5}{6}$$

$$=\frac{12-36+25}{30}$$

$$=\frac{1}{30}$$

Hence, the correct answer is Option C