To solve for \( x \) in the equation
\[ -\frac{5}{2}x = -14, \]
we can first eliminate the negative sign from both sides:
\[ \frac{5}{2}x = 14. \]
Next, we can isolate \( x \) by multiplying both sides by the reciprocal of \(\frac{5}{2}\), which is \(\frac{2}{5}\):
\[ x = 14 \cdot \frac{2}{5}. \]
Now, calculate \( 14 \cdot \frac{2}{5} \):
\[ x = \frac{28}{5}. \]
Therefore, the simplified solution for \( x \) is
\[ \boxed{\frac{28}{5}}. \]