\( 5 \frac{2}{7} - 1 \frac{2}{22} = 5 \frac{2}{7} - 1 \frac{1}{11} = \frac{37}{7} - \frac{12}{11} = \frac{37 \cdot 11 - 12 \cdot 7}{77} = \frac{407 - 84}{77} = \frac{323}{77} \)