To solve the equation \( \frac{8}{5} x = -10 \), we will isolate \( x \) by multiplying both sides by the reciprocal of \( \frac{8}{5} \), which is \( \frac{5}{8} \).
Starting with the equation:
\[ \frac{8}{5} x = -10 \]
Multiply both sides by \( \frac{5}{8} \):
\[ x = -10 \cdot \frac{5}{8} \]
Now we can calculate the right-hand side:
\[ x = -10 \cdot \frac{5}{8} = \frac{-50}{8} \]
We can simplify \( \frac{-50}{8} \):
\[ \frac{-50}{8} = \frac{-25}{4} \]
Thus, the solution to the equation \( \frac{8}{5} x = -10 \) is:
\[ \boxed{-\frac{25}{4}} \]