Calculate the value of \(k\) for which the line \(y = 2x + k\) is a tangent to the curve \(y = 2x^2 - 4x + 5\).

The blue parabola here is \(y = 2x^2 - 4x + 5\), while the red line is \(y = 2x + k\).

The blue parabola here is \(y = 2x^2 - 4x + 5\), while the red line is \(y = 2x + k\).