To solve the quadratic equation \(x^2 - 2x + 5 = 0\), we can use the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In our equation, \(a = 1\), \(b = -2\), and \(c = 5\). Substituting these values into the formula gives:
\[ x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4 \cdot 1 \cdot 5}}{2 \cdot 1} \] \[ x = \frac{2 \pm \sqrt{4 - 20}}{2} \] \[ x = \frac{2 \pm \sqrt{-16}}{2} \] \[ x = \frac{2 \pm 4i}{2} \] \[ x = 1 \pm 2i \]
Thus, the solutions are:
\[ x = 1 + 2i \quad \text{and} \quad x = 1 - 2i \]
So the correct response is \(1 \pm 2i\).