\[\left( \frac{3}{8} + \left( \frac{1}{2} \right)^{2} + 1\frac{1}{4} \right)\ :\frac{5}{3} =\]
\[= \left( \frac{3}{8} + \frac{1^{\backslash 2}}{4} + \frac{5^{\backslash 2}}{4} \right) \cdot \frac{3}{5} =\]
\[= \frac{3 + 2 + 10}{8} \cdot \frac{3}{5} =\]
\[= \frac{15 \cdot 3}{8 \cdot 5} = \frac{9}{8} = 1\frac{1}{8}.\]