To express \(x^2 - 4x + 5\) in the form \((x + a)^2 + b\), we complete the square:

Start with the expression:

\(x^2 - 4x + 5\)

Take half of the coefficient of \(x\), square it, and add and subtract it inside the expression:

\(x^2 - 4x + 4 - 4 + 5\)

Rewrite as a perfect square:

\((x - 2)^2 + 1\)

Thus, the expression in the form \((x + a)^2 + b\) is \((x - 2)^2 + 1\).

The minimum point occurs at \(x = 2\), giving the coordinates \((2, 1)\).