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Let \( f: R \rightarrow R \) be a continuous and differentiable function such that \( \left(f\left(x^{2}+1\right)\right)^{\sqrt{x}}=5 \) for \( \forall x \in(0, \infty) \). Then the value of \( \left(f\left(\frac{16+y^{2}}{y^{2}}\right)\right)^{\frac{4}{\sqrt{y}}} \) for \( y \in(0, \infty) \) is equal to
(A) 5
(B) 25
(C) 125
(D) 625
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