\[\boxed{\text{5.\ 51}}\]
\[\textbf{а)}\ - \frac{5}{6}x \cdot \left( - \frac{1}{5}y \right) = \frac{1}{6}\text{xy} \rightarrow \frac{1}{6}\]
\[\textbf{б)} - \frac{4}{7}a \cdot \left( - \frac{7}{8}a \right) = \frac{1}{2}a^{2} \rightarrow \frac{1}{2}\]
\[\textbf{в)} - \frac{20}{9}x \cdot \left( - \frac{9}{4}z \right) = 5xz \rightarrow 5\]
\[\textbf{г)}\ \frac{5}{12}x \cdot \left( - \frac{4}{15}y \right) =\]
\[= - \frac{1}{9}\text{xy} \rightarrow - \frac{1}{9}\]
\[\textbf{д)}\ \frac{3}{8}n \cdot \left( - \frac{7}{6}b \right) \cdot \frac{2}{7}z =\]
\[= - \frac{3}{8}n \cdot \frac{1}{3}bz = - \frac{1}{8}\text{nbz} \rightarrow - \frac{1}{8}\]
\[\textbf{е)}\ \frac{5}{9}a \cdot \frac{9}{20}b \cdot 3z = \frac{1}{4}ab \cdot 3z =\]
\[= \frac{3}{4}\text{abz} \rightarrow \frac{3}{4}\ \]