Answer
The value of given expression $f\left( -x \right)-f\left( x \right)$ is $-2{{x}^{3}}-2x$.
Work Step by Step
By replacing –x by x in the given expression, we get the following expression
$\begin{align}
& f\left( -x \right)={{\left( -x \right)}^{3}}+\left( -x \right)-5 \\
& =-{{x}^{3}}-x-5
\end{align}$
So, calculate the value of the expression $f\left( -x \right)-f\left( x \right)$ as follows
$\begin{align}
& f\left( -x \right)-f\left( x \right)=-{{x}^{3}}-x-5-\left( {{x}^{3}}+x-5 \right) \\
& =-{{x}^{3}}-x-5-{{x}^{3}}-x+5 \\
& =-2{{x}^{3}}-2x
\end{align}$
Therefore, the value of the expression $f\left( -x \right)-f\left( x \right)$ is $-2{{x}^{3}}-2x$.
