To solve the equation \( \frac{5}{2}x = -\frac{1}{8} \), you can follow these steps:
- Multiply both sides by the reciprocal of \( \frac{5}{2} \), which is \( \frac{2}{5} \).
\[ x = -\frac{1}{8} \cdot \frac{2}{5} \]
- Perform the multiplication:
\[ x = -\frac{2}{40} \]
- Simplify the fraction:
\[ x = -\frac{1}{20} \]
Thus, the solution to the equation \( \frac{5}{2}x = -\frac{1}{8} \) is
\[ \boxed{-\frac{1}{20}}. \]