Решение

a) $$5\frac{1}{4}:1\frac{1}{5}+7:\frac{2}{3} = \frac{21}{4} : \frac{6}{5} + 7 \cdot \frac{3}{2} = \frac{21}{4} \cdot \frac{5}{6} + \frac{21}{2} = \frac{21 \cdot 5}{4 \cdot 6} + \frac{21}{2} = \frac{105}{24} + \frac{21}{2} = \frac{105 + 21 \cdot 12}{24} = \frac{105 + 252}{24} = \frac{357}{24} = \frac{119}{8} = 14\frac{7}{8}$$.

Ответ: $$14\frac{7}{8}$$