To solve the equation
\[ -x^2 - 3x = 5 - 3x, \]
we start by simplifying it. First, we can add \(3x\) to both sides of the equation:
\[ -x^2 - 3x + 3x = 5 - 3x + 3x, \]
which simplifies to:
\[ -x^2 = 5. \]
Next, we can multiply both sides by \(-1\) to isolate \(x^2\):
\[ x^2 = -5. \]
Now, we take the square root of both sides. Remember that the square root of a negative number involves the imaginary unit \(i\):
\[ x = \pm \sqrt{-5} = \pm \sqrt{5} i. \]
Thus, the solutions to the equation can be consolidated as:
\[ x = \sqrt{5} i \quad \text{or} \quad x = -\sqrt{5} i. \]
The final answer expressed as complex numbers is:
\[ x = \sqrt{5} i, \quad x = -\sqrt{5} i. \]