1. **State the problem:** We are given a point $(4, -5)$ and a linear equation $2x - 5y = -10$. We want to check if the point lies on the line represented by the equation. 2. **Formula and rule:** To check if a point $(x_0, y_0)$ lies on a line given by $Ax + By = C$, substitute $x_0$ and $y_0$ into the equation and see if the equality holds. 3. **Substitute the point into the equation:** $$2(4) - 5(-5) = ? -10$$ 4. **Calculate the left side:** $$8 + 25 = 33$$ 5. **Compare with the right side:** $$33 \neq -10$$ 6. **Conclusion:** Since $33$ is not equal to $-10$, the point $(4, -5)$ does not lie on the line $2x - 5y = -10$.