To express \(x^2 + 6x + 5\) in the form \((x + a)^2 + b\), we complete the square:

Start with the expression: \(x^2 + 6x + 5\).

1. Take half of the coefficient of \(x\), which is 6, giving 3, and square it: \(3^2 = 9\).

2. Add and subtract this square inside the expression:

\(x^2 + 6x + 9 - 9 + 5\).

3. Rewrite the expression as a perfect square and a constant:

\((x + 3)^2 - 4\).

Thus, \(a = 3\) and \(b = -4\).