\[\boxed{\text{5.459.}}\]
\[\textbf{а)}\ \frac{4}{7} \cdot 14 = \frac{4 \cdot 14}{7} = 4 \cdot 2 = 8\]
\[\textbf{б)}\ 2 \cdot \frac{5}{8} = \frac{2 \cdot 5}{8} = \frac{5}{4} = 1\frac{1}{4}\]
\[\textbf{в)}\ 10 \cdot \frac{3}{8} = \frac{10 \cdot 3}{8} = \frac{5 \cdot 3}{4} = \frac{15}{4} =\]
\[= 3\frac{3}{4}\]
\[\textbf{г)}\ \frac{3}{7} \cdot 21 = \frac{3 \cdot 21}{7} = 3 \cdot 3 = 9\]
\[\textbf{д)}\ \frac{9}{17} \cdot 0 = 0\]
\[\textbf{е)}\ \frac{11}{100} \cdot 1 = \frac{11}{100}\]
\[\textbf{ж)}\ \frac{1}{3} \cdot 24 = \frac{24}{3} = 8\]
\[\textbf{з)}\ \frac{1}{31} \cdot 31 = \frac{31}{31} = 1\]