Given the function $g\left(x\right)=\frac{18}{x^2}$, find $g^{\prime }\left(x\right)$ using the limit definition of the derivative. Then, calculate the value of $g^{\prime }\left(5\right)$.

$g^{\prime}(x)=-\frac{36}{x^3}$

$g^{\prime}(5)=-\frac{36}{125}$

$g^{\prime}(x)=-\frac{36}{x^3}$

$g^{\prime }\left(5\right)=-\frac{36}{225}$

$g^{\prime }\left(x\right)=\frac{36}{x^2}$

$g^{\prime }\left(5\right)=\frac{36}{25}$

$g^{\prime}(x)=\frac{36}{x^2}$

$g^{\prime }\left(5\right)=\frac{36}{125}$