\[\boxed{\text{5.463.}}\]
\[\textbf{а)}\ \frac{4}{7} \cdot \frac{7}{25} = \frac{4}{25}\]
\[\textbf{б)}\ \frac{2}{3} \cdot \frac{9}{8} = \frac{1 \cdot 3}{1 \cdot 4} = \frac{3}{4}\]
\[\textbf{в)}\ \frac{4}{11} \cdot \frac{11}{4} = 1\]
\[\textbf{г)}\ \frac{21}{8} \cdot \frac{13}{14} = \frac{3 \cdot 13}{8 \cdot 2} = \frac{39}{16} = 2\frac{7}{16}\]
\[\textbf{д)}\ \frac{2}{11} \cdot \frac{3}{4} = \frac{1 \cdot 3}{11 \cdot 2} = \frac{3}{22}\]
\[\textbf{е)}\ \frac{10}{3} \cdot \frac{7}{100} = \frac{1 \cdot 7}{3 \cdot 10} = \frac{7}{30}\]