To find the values of \(b\) for which the line meets the curve, set the equations equal to each other:

\(x + 1 = x^2 + bx + 5\)

Rearrange to form a quadratic equation:

\(x^2 + (b-1)x + 4 = 0\)

For the line to meet the curve, the quadratic must have real roots. This requires the discriminant to be non-negative:

\((b-1)^2 - 4 \times 1 \times 4 \geq 0\)

\((b-1)^2 - 16 \geq 0\)

\((b-1)^2 \geq 16\)

Taking square roots gives:

\(b-1 \geq 4\) or \(b-1 \leq -4\)

Solving these inequalities:

\(b \geq 5\) or \(b \leq -3\)

Thus, the set of values for \(b\) is \(b \geq 5\) or \(b \leq -3\).