1. **State the problem:** We are given the differential equation $y'(x) = -5y(x)$ and need to find the general solution. 2. **Formula and rules:** This is a first-order linear differential equation of the form $y' = ky$ where $k$ is a constant. The general solution is given by: $$y(x) = Ce^{kx}$$ where $C$ is an arbitrary constant. 3. **Apply the formula:** Here, $k = -5$, so the solution is: $$y(x) = Ce^{-5x}$$ 4. **Explanation:** The function $y(x)$ changes at a rate proportional to its current value, with a proportionality constant of $-5$. This means $y(x)$ decays exponentially as $x$ increases. 5. **Final answer:** $$\boxed{y(x) = Ce^{-5x}}$$