To determine which of the options is equivalent to \( \frac{1}{8^5} \), let's simplify \( \frac{1}{8^5} \):
\[ \frac{1}{8^5} = 8^{-5} \]
Now let's analyze the options provided:
- \( 8 \frac{1}{5} \): This is not in exponent form and does not equal \( \frac{1}{8^5} \).
- \( 5^{-8} \): This does not relate to \( 8^5 \) or its reciprocal.
- \( 8^{-5} \): This is exactly what we found: \( \frac{1}{8^5} = 8^{-5} \).
- \( 8^5 \): This is not equivalent to \( \frac{1}{8^5} \); it's the opposite in terms of value.
Thus, the correct answer is:
\( 8^{-5} \)