Let $f(x) = x^3 + 2x^2 + 3x + 2$ and $g(x)$ be a polynomial with integer coefficients. When $f(x)$ is divided by $g(x)$, it leaves quotient $q(x)$ and remainder $r(x)$, both of which have integer coefficients.

If $q(x) = r(x) \neq 1$ ,then find $g(5)$.

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