Given that $\dfrac{5^x}{2^{2x} \times 5^{3 - x}} = 2^m 5^n$, express $m$ and $n$ in terms of $x$.

1. Separate the denominator powers and move them to the numerator using negative indices.

$\frac{5^x}{2^{2x}\times 5^{3-x}}=5^x\times 2^{-2x}\times 5^{-(3-x)}$

2. Combine the powers of 5 and compare indices with $2^m5^n$.

$5^x\times 2^{-2x}\times 5^{-(3-x)}=2^{-2x}\times 5^{x-(3-x)}$
$=2^{-2x}\times 5^{2x-3}$
Comparing with $2^m5^n$,
$m=-2x,\qquad n=2x-3.$