Answer
$y=\frac{1}{2}\cdot(x-3)^2+3$
Work Step by Step
The vertex form of the parabola is $y=a(x-3)^2+3$ and if $x=5, y=5$, so
$$
\begin{aligned}
5 & =a(5-3)^2+3 \\
2 & =4 a \\
a& =\frac{1}{2}
\end{aligned}
$$ Hence $y=\frac{1}{2}\cdot(x-3)^2+3$.
