\[5\frac{2}{5} \cdot 8\frac{4}{7} - 5\frac{2}{5} \cdot 6\frac{4}{7} =\]
\[= 5\frac{2}{5} \cdot \left( 8\frac{4}{7} - 6\frac{4}{7} \right) = \frac{27}{2} \cdot 2 = 27.\]