IT-CESENATICO 2012 Problem 4

Let $x_1,x_2,x_3, \cdots$ be a sequence defined by the following recurrence relation: $$\begin{cases}x_{1}&= 4 x_{n+1}&= x_{1}x_{2}x_{3}\cdots x_{n}+5\text{ for }n\ge 1\end{cases}$$ The first few terms of the sequence are $x_1=4,x_2=9,x_3=41 \cdots$ Find all pairs of positive integers $\{a,b\}$ such that $x_a x_b$ is a perfect square.