#### Answer

The complete statement is: The degree of the polynomial function $f\left( x \right)=-2{{x}^{3}}\left( x-1 \right)\left( x+5 \right)$ is $5$. The leading coefficient is $-2$.

#### Work Step by Step

Consider the polynomial function:
$f\left( x \right)=-2{{x}^{3}}\left( x-1 \right)\left( x+5 \right)$
The degree of factor $2{{x}^{3}}$ is 3 and the leading coefficient is $-2$
The degree of factor $\left( x-1 \right)$ is 1 and the leading coefficient is 1.
The degree of factor $\left( x+5 \right)$ is 1 and the leading coefficient is 1.
Therefore, the degree of $f\left( x \right)$ is $3+1+1$ that is 5 and the leading coefficient is $-2\cdot 1\cdot 1$ that is $-2$
The degree, $n=5$ and the leading coefficient, $-2$.
Hence, the degree of the polynomial function $f\left( x \right)=-2{{x}^{3}}\left( x-1 \right)\left( x+5 \right)$ is $5$. The leading coefficient is $-2$.