MathNet 2011 Question 3

A sequence of integers $\{a_{i}\}$ is defined as follows: $a_{i} = i$ for all $1 \leq i \leq 5$, and $a_{i} = a_{1} a_{2} \cdots a_{i-1} - 1$ for all $i \gt 5$. Evaluate $a_{1} a_{2} \cdots a_{2011} - \sum_{i=1}^{2011} a_{i}^{2}$.