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

\(f(x) = (x-1)^2 + 4\).

For \(g(x) = x^2 + 4x + 13\), complete the square:

\(g(x) = (x+2)^2 + 9\).

Now express \(g(x)\) in the form \(f(x+p) + q\):

\(g(x) = (x+2)^2 + 9 = ((x+3)-1)^2 + 4 + 5 = f(x+3) + 5\).

Thus, \(p = 3\) and \(q = 5\).

(b) The transformation from \(y = f(x)\) to \(y = g(x)\) is a translation. The completed square forms show a horizontal shift by \(-3\) and a vertical shift by \(5\). Therefore, the transformation is a translation by \(\begin{pmatrix} -3 \\ 5 \end{pmatrix}\).