$a)5\cdot \frac{5}{7}=\frac{5\cdot 5}{7}=\frac{25}{7}=3\frac{4}{7}$  

$b)3\cdot \frac{2}{5}=\frac{3\cdot 2}{5}=\frac{6}{5}=1\frac{1}{5}$  

$c)4\cdot \frac{5}{6}=\frac{4\cdot 5}{6}=\frac{20}{6}=3\frac{2}{6}=3\frac{1}{3}$  

$d)12\cdot \frac{3}{5}=\frac{12\cdot 3}{5}=\frac{36}{5}=7\frac{1}{5}$  

$e)\frac{7}{10}\cdot 8=\frac{7\cdot 8}{10}=\frac{56}{10}=5\frac{6}{10}=5\frac{3}{5}$  

$f)\frac{3}{4}\cdot 15=\frac{3\cdot 15}{4}=\frac{45}{4}=11\frac{1}{4}$