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The derivative \( f'(x) = rac{-5}{(x - 1)^2} \) is always negative for all \( x
eq 1 \), indicating that \( f(x) \) is a decreasing function on its domain. Thus, \( f(x) \) does not have a maximum in the traditional sense but decreases towards \(-\infty\) as \( x o 1^+ \) and increases without bound as \( x o \infty \). Therefore, there is no finite \( x \) that maximizes \( f(x) \).
oxed{ ext{No finite maximum exists}}

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