A Cool Functional Equation

Algebra Level 5

Let \(f(x)\) be a polynomial with real coefficients such that \(f(0) = 1,\) \(f(2)+f(3)=125,\) and for all \(x\), \(f(x)f(2x^{2})=f(2x^{3}+x).\) Find \(f(5).\)

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