\[\boxed{\text{5.558.}}\]
\[\textbf{а)}\ \frac{7}{9}\ :\frac{7}{18} = \frac{7}{9} \cdot \frac{18}{7} = 2\]
\[\textbf{б)}\ \frac{1}{4}\ :\frac{1}{3} = \frac{1}{4} \cdot 3 = \frac{3}{4}\]
\[\textbf{в)}\ \frac{3}{4}\ :\frac{7}{9} = \frac{3}{4} \cdot \frac{9}{7} = \frac{27}{28}\]
\[\textbf{г)}\ \frac{3}{7}\ :\frac{1}{14} = \frac{3}{7} \cdot 14 = 3 \cdot 2 = 6\]
\[\textbf{д)}\ \frac{6}{11}\ :6 = \frac{6}{11} \cdot \frac{1}{6} = \frac{1}{11}\]
\[\textbf{е)}\ \frac{9}{13}\ :3 = \frac{9}{13} \cdot \frac{1}{3} = \frac{3}{13}\]
\[\textbf{ж)}\ \frac{5}{7}\ :\frac{1}{7} = \frac{5}{7} \cdot 7 = 5\]
\[\textbf{з)}\ \frac{15}{22}\ :5 = \frac{15}{22} \cdot \frac{1}{5} = \frac{3}{22}\]