Answer
$(x-5)$
Work Step by Step
When we multiply the numerator and denominator of a rational expression with a nonzero expression,
we are multiplying the rational expression with 1.
Multiplying with 1 does not change the value, so the resulting rational expression is equivalent to the initial one..
Here, we have: initial rational expression = $\displaystyle \frac{x}{(x+5)}$.
Multiply it with $1=\displaystyle \frac{A}{A}$, where A is some nonzero expression:
$\displaystyle \frac{x}{(x+5)}\cdot\frac{A}{A}=\frac{x\cdot A}{(x+5)\cdot A}$
We want the resulting denominator to be $x^{2}-25.$
$ x^{2}-25=(x+5)(x-5)\qquad$ ... we recognized a difference of squares...
so, $A=(x-5)$ and
$\displaystyle \frac{x}{(x+5)}=\frac{x(x-5)}{(x+5)(x-5)}=\frac{x(x-5)}{x^{2}-25}$
