\[\frac{5}{7} = \frac{5 \cdot 5}{7 \cdot 5} = \frac{25}{35}\]
\[\frac{25}{35} - \frac{3}{35} = \frac{25-3}{35} = \frac{22}{35}\]
\[\frac{22}{35} \cdot \frac{7}{44} = \frac{22 \cdot 7}{35 \cdot 44} = \frac{2 \cdot 1}{5 \cdot 4} = \frac{2}{20} = \frac{1}{10}\]
Ответ: \(\frac{1}{10}\)