Answer
$(25,-20)$
Work Step by Step
The standard form of the given quadratic function, $f(x)=
-x^2+10x+5
,$ is
\begin{array}{l}\require{cancel}
f(x)=\left( -x^2+10x \right)+5
\\\\
f(x)=-\left( x^2-10x \right)+5
\\\\
f(x)=-\left( x^2-10x+\left( \dfrac{-10}{2} \right)^2 \right)+5-\left( \dfrac{-10}{2} \right)^2
\\\\
f(x)=-\left( x^2-10x+25 \right)+5-25
\\\\
f(x)=-\left( x-25 \right)^2-20
.\end{array}
Since the vertex of $f(x)=a(x-h)^2+k$ is at $(h,k)$, then the vertex of the equation above is
\begin{array}{l}\require{cancel}
(25,-20)
.\end{array}
