Answer
The graph of $f\left( x \right)={{\left( x+5 \right)}^{2}}+3$ has its vertex at $\left( 5,3 \right)$. False.
Work Step by Step
For the standard equation of the parabola $f\left( x \right)=a{{\left( x-h \right)}^{2}}+k$ , the vertex is $\left( h,k \right)$. So, consider the given function
$\begin{align}
& f\left( x \right)={{\left( x+5 \right)}^{2}}+3 \\
& ={{\left( x-\left( -5 \right) \right)}^{2}}+3
\end{align}$
Equate to the standard equation,
$h=-5\text{ and }k=3$,vertex is at $\left( -5,3 \right)$.
