The simplified value of $$\left[1\frac{1}{5}  of  \left\{\frac{3}{7} - \left(1\frac{4}{15}-\frac{13}{15}\right) \times \frac{5}{7}\right\}\right] \div \left(\frac{6}{7} \div 5\right)$$ is:

$$\left[1\frac{1}{5}  of  \left\{\frac{3}{7} - \left(1\frac{4}{15}-\frac{13}{15}\right) \times \frac{5}{7}\right\}\right] \div \left(\frac{6}{7} \div 5\right)$$ 

$$\left[1\frac{1}{5}  of  \left\{\frac{3}{7} - \left(1\frac{4}{15}-\frac{13}{15}\right) \times \frac{5}{7}\right\}\right] \div \left(\frac{6}{35} \right)$$ 

$$\left[1\frac{1}{5}  of  \left\{\frac{3}{7} - \left(\frac{19}{15}-\frac{13}{15}\right) \times \frac{5}{7}\right\}\right] \div \left(\frac{6}{35} \right)$$ 

$$\left[1\frac{1}{5}  of  \left\{\frac{3}{7} - \left(\frac{6}{15}\right) \times \frac{5}{7}\right\}\right] \div \left(\frac{6}{35} \right)$$ 

$$\left[1\frac{1}{5}  of  \left\{\frac{3}{7} - \frac{2}{7} \right\}\right] \div \left(\frac{6}{35} \right)$$ 

$$\frac{6}{5}\times\frac{1}{7}\times\frac{35}{6}=1$$