5. Let $f(x)$ be an even function defined on $(-\infty,+\infty)$ with a period of 2. On the interval $[2,3]$, $f(x)=-2(x-3)^{2}+4$.
(1) When $x \in[1,2]$, find the analytical expression for $f(x)$;
(II) If the rectangle $A B C D$ has two vertices $A$ and $B$ on the $x$-axis, and $C, D$ on the graph of the function $y=f(x)(0 \leqslant x \leqslant 2)$, find the maximum area of the rectangle $A B C D$.
$\begin{array}{l}\text { ((I) } f(x)=-2(x-1)^{2}+4(1 \leqslant x \leqslant 2),(\text { II) } \\ \left.\frac{16 \sqrt{6}}{4} .\right)\end{array}$