5. The function $f(x)$ at each point $x$ takes a value equal to the maximum of the expression $(x+2) y^{2}+(3-2 x) y+3 x+a$ with respect to the variable $y$ on the interval $[1 ; 4]$. For what values of $a$ does the inequality $f(x) \geq 0$ hold for all $x \geq -3$?
Problem 5. Answer: $a \in[-11 ;+\infty)$