Вычислите: \(\left(5\frac{1}{16}-1\frac{1}{8}\right)\left(\frac56+\frac3{14}\right)\).

\[5\frac1{16}-1\frac18=\frac{81}{16}-\frac{18}{16}=\frac{63}{16}.\]

\[\frac56+\frac3{14}=\frac{35}{42}+\frac9{42}=\frac{44}{42}=\frac{22}{21}.\]

\[\frac{63}{16}\cdot\frac{22}{21}=\frac{3\cdot22}{16}=\frac{66}{16}=\frac{33}{8}=4\frac18.\]

Ответ: \(4\frac18\).