To solve the equation \( \frac{8}{5}x = -10 \), we first isolate \( x \).
- Multiply both sides of the equation by \( \frac{5}{8} \) to eliminate the fraction:
\[ x = -10 \cdot \frac{5}{8} \]
- Calculate the right-hand side:
\[ x = -\frac{10 \cdot 5}{8} = -\frac{50}{8} \]
- Simplify \( -\frac{50}{8} \):
\[ x = -\frac{25}{4} \]
Thus, the solution of the equation \( \frac{8}{5}x = -10 \) is:
\[ \boxed{-\frac{25}{4}} \]