Step 1: Solving the quadratic equation.
The given quadratic equation is \( x^2 + 2x - 5 = 0 \). Using the quadratic formula, we find the values of \( x \) as \( x = -2, 2, 4 \).
Step 2: Conclusion.
The correct values of \( x \) are \( -2, 2, 4 \), corresponding to option (2).