MathNet 2014 Question 57

Let $a_1, b_1, c_1, a_2, b_2, c_2$ be positive real numbers such that $b_1^2 \le 4a_1c_1$ and $b_2^2 \le 4a_2c_2$. Prove that $4(a_1 + a_2 + 5)(c_1 + c_2 + 1) \gt (b_1 + b_2 + 2)^2$. (Macedonia 2013)