Let the first term be \( a \), and the common ratio be \( r \). Given:

- Second term: \( ar = 1 \)
- Fifth term: \( ar^4 = \frac{1}{8} \)

From the first equation, we have: \(a = \frac{1}{r}\)

Substituting into the second equation:

\(\frac{1}{r} r^4 = \frac{1}{8}\)
\(r^3 = \frac{1}{8}\)

Taking the cube root gives:

\(r = \frac{1}{2}\)

Thus, the common ratio is \(\frac{1}{2}\)