#### Answer

$-32x^{15}y^{10}$

#### Work Step by Step

We are given the expression $(-2x^{3}y^{2})^{5}$. We can simplify this expression using the power rule, which holds that $(a^{m})^{n}=a^{m\times n}$ (where a is a real number, and m and n are integers).
$(-2x^{3}y^{2})^{5}=(-2)^{5}\times(x^{3})^{5}\times(y^{2})^{5}=-32x^{15}y^{10}$