Question: Suppose \(f\) is a differentiable function such that \(\lim _{x \rightarrow 5^{+}} f(x)=1\) and \(\lim _{x \rightarrow 5^{+}} f^{\prime}(x)=4\).

1. Showing all work, analytically determine the exact value of
   \[\lim _{x \rightarrow 5^{+}}(f(x))^{\frac{1}{7 x-35}}\]
2. Round your answer from a) to 3 decimal places and enter it below.

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