\[\boxed{\text{5.486.}}\]
\[\textbf{а)}\ \frac{8}{9} \cdot \frac{3}{4} = \frac{2 \cdot 1}{3 \cdot 1} = \frac{2}{3}\]
\[\textbf{б)}\ \frac{11}{45} \cdot \frac{9}{22} = \frac{1 \cdot 1}{5 \cdot 2} = \frac{1}{10}\]
\[\textbf{в)}\ \frac{51}{29} \cdot \frac{58}{85} = \frac{3 \cdot 2}{1 \cdot 5} = \frac{6}{5} = 1\frac{1}{5}\]
\[\textbf{г)}\ \frac{1}{4} \cdot \frac{4}{5} \cdot \frac{5}{6} = \frac{1}{6}\]