'Rooty' polynomials!(part 2)

Algebra Level 3

Let f(x)=x3+2x2+3x+2f(x) = x^3 + 2x^2 + 3x + 2 and g(x)g(x) be a polynomial with integer coefficients. When f(x)f(x) is divided by g(x)g(x), it leaves quotient q(x)q(x) and remainder r(x)r(x), both of which have integer coefficients.

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

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