解:
$\begin{aligned}&[-4^{2}\times(-\frac{1}{4})^{2}-0.8]\div(-5\frac{2}{5})\\=&[-16\times\frac{1}{16}-0.8]\div(-\frac{27}{5})\\=&(-1 - 0.8)\div(-\frac{27}{5})\\=&(-\frac{9}{5})\div(-\frac{27}{5})\\=&(-\frac{9}{5})\times(-\frac{5}{27})\\=&\frac{1}{3}\end{aligned}$