Compute
\[
\lim_{n\to\infty}\frac{5+55+\cdots+\overbrace{55\ldots 5}^{n\text{ digits }}}{10^n}
\]

Compute
\[
\lim_{n\to\infty}\frac{5+55+\cdots+\overbrace{55\ldots 5}^{n\text{ digits }}}{10^n}
\]

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