#### Answer

$5x^2y^3 \left( 2y^3-1-5x^3 \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Get the $GCF$ of the given expression, $
10x^2y^5-5x^2y^3-25x^5y^3
.$ Divide the given expression and the $GCF.$ Express the answer as the product of the $GCF$ and the resulting quotient.
$\bf{\text{Solution Details:}}$
The $GCF$ of the constants of the terms $\{
10,5,25
\}$ is $
5
$ since it is the highest number that can divide all the given constants. The $GCF$ of the common variable/s is the variable/s with the lowest exponent. Hence, the $GCF$ of the common variable/s $\{
x^2y^5,x^2y^3,x^5y^3
\}$ is $
x^2y^3
.$ Hence, the entire expression has $GCF=
5x^2y^3
.$
Factoring the $GCF=
5x^2y^3
,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
5x^2y^3 \left( \dfrac{10x^2y^5}{5x^2y^3}-\dfrac{5x^2y^3}{5x^2y^3}-\dfrac{25x^5y^3}{5x^2y^3} \right)
\\\\=
5x^2y^3 \left( 2y^3-1-5x^3 \right)
.\end{array}