解:
$\begin{aligned}\sqrt{15}×\frac{5}{2}\sqrt{2\frac{2}{5}}÷5\sqrt{\frac{1}{5}}&=\sqrt{15}×\frac{5}{2}\sqrt{\frac{12}{5}}÷5\sqrt{\frac{1}{5}}\\&=(\frac{5}{2}÷5)×\sqrt{15×\frac{12}{5}÷\frac{1}{5}}\\&=\frac{1}{2}×\sqrt{15×\frac{12}{5}×5}\\&=\frac{1}{2}×\sqrt{180}\\&=\frac{1}{2}×6\sqrt{5}\\&=3\sqrt{5}\end{aligned}$