1) $$\frac{5}{6} \cdot \frac{7}{9} = \frac{5 \cdot 7}{6 \cdot 9} = \frac{35}{54}$$.
2) $$\frac{3}{8} : \frac{9}{16} = \frac{3}{8} \cdot \frac{16}{9} = \frac{3 \cdot 16}{8 \cdot 9} = \frac{1 \cdot 2}{1 \cdot 3} = \frac{2}{3}$$.
3) $$2\frac{5}{11} \cdot 2\frac{4}{9} = \frac{27}{11} \cdot \frac{22}{9} = \frac{27 \cdot 22}{11 \cdot 9} = \frac{3 \cdot 2}{1 \cdot 1} = 6$$.
4) $$\frac{15}{16} : 5 = \frac{15}{16} \cdot \frac{1}{5} = \frac{15 \cdot 1}{16 \cdot 5} = \frac{3 \cdot 1}{16 \cdot 1} = \frac{3}{16}$$.
5) $$14 : \frac{7}{8} = 14 \cdot \frac{8}{7} = \frac{14 \cdot 8}{7} = \frac{2 \cdot 8}{1} = 16$$.