We start with the expression \( 5(-x)^{2} + 8(-x) - 2 \). First, we square the term \((-x)\), which gives us \( (-x)^{2} = x^{2} \). Therefore, the expression simplifies to:
\[
5x^{2} + 8(-x) - 2 = 5x^{2} - 8x - 2
\]
Step 2: Final Form of the Expression
The simplified expression is now \( 5x^{2} - 8x - 2 \). This is the final form of the expression after simplification.