Know the functioning of the function?

Algebra Level 4

Let f(x)f(x) be a polynomial. It is known that for all xx,

f(x)f(2x2)=f(2x3+x)\large f(x)f(2x^2) = f(2x^3+x)

If f(0)=1f(0)=1 and f(2)+f(3)=125f(2)+f(3)=125, find f(5)f(5).

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