3.82: Descending binomial product: find $a$, $b$, $c$

The first three terms, in descending powers of $x$, of the expansion of $\left(ax + \dfrac{2}{5}\right)^{5}\left(1 - \dfrac{b}{x}\right)^{2}$ can be written as $32x^{5} - 160x^{4} + cx^{3}$, where $a$, $b$ and $c$ are constants. Find the exact values of $a$, $b$ and $c$.