1. The problem is to find the sum of two complex numbers $z_1 = -1 + 2i$ and $z_2 = 2 + 3i$. 2. The formula for adding complex numbers is: $$z_1 + z_2 = (a + bi) + (c + di) = (a + c) + (b + d)i$$ where $a, b, c, d$ are real numbers. 3. Applying the formula: $$z_1 + z_2 = (-1 + 2i) + (2 + 3i) = (-1 + 2) + (2 + 3)i$$ 4. Simplify the real and imaginary parts: $$= 1 + 5i$$ 5. Therefore, the sum of $z_1$ and $z_2$ is: $$\boxed{1 + 5i}$$