The limit of the expression you provided is:

$\lim_{x \to 1} \frac{x^4 - 2x + 1}{x^5 - 1} = \frac{2}{5}$

This was obtained using L'Hôpital's Rule due to the initial indeterminate form $\frac{0}{0}$ when directly substituting $x = 1$.

If you need further explanation or have any other questions, feel free to ask!

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Here are 5 related questions:

1. How can you determine if L'Hôpital's Rule is the best method to solve a limit?
2. What are some common indeterminate forms that arise when solving limits?
3. Can you always use direct substitution for evaluating limits?
4. How does the behavior of a function near a point differ from the function's actual value at that point?
5. How would the problem change if the limit was as $x \to \infty$ instead of $x \to 1$?

Tip: Always check for indeterminate forms first when evaluating limits, as this will guide you towards the most appropriate method for solving the problem.