\[\boxed{\text{5.524.}}\]
\[\textbf{а)}\ \frac{5}{9}\ :5 = \frac{5}{9} \cdot \frac{1}{5} = \frac{1}{9}\]
\[\textbf{б)}\ \frac{4}{7}\ :4 = \frac{4}{7} \cdot \frac{1}{4} = \frac{1}{7}\]
\[\textbf{в)}\ 1\ :\frac{5}{13} = 1 \cdot \frac{13}{5} = 2\frac{3}{5} = 2,6\]
\[\textbf{г)}\ 7\ :\frac{4}{7} = 7 \cdot \frac{7}{4} = \frac{49}{4} = 12\frac{1}{4}\]
\[\textbf{д)}\ 4\ :\frac{8}{9} = 4 \cdot \frac{9}{8} = \frac{9}{2} = 4\frac{1}{2} = 4,5\]