Let the coordinates of point B be \((x, y)\).

Given that \(\vec{a}\) is the position vector of the point \((2, -3)\), so \(\vec{a} = \begin{pmatrix} 2 \\ -3 \end{pmatrix}\).

Also, \(\vec{AB} = \vec{a}\), where A has coordinates \((-4, 5)\).

We can express \(\vec{AB}\) as the difference between the position vectors of B and A:

\(\vec{AB} = \vec{OB} - \vec{OA}\), where \(\vec{OB} = \begin{pmatrix} x \\ y \end{pmatrix}\) and \(\vec{OA} = \begin{pmatrix} -4 \\ 5 \end{pmatrix}\).

So, \(\begin{pmatrix} x \\ y \end{pmatrix} - \begin{pmatrix} -4 \\ 5 \end{pmatrix} = \begin{pmatrix} 2 \\ -3 \end{pmatrix}\).

This implies \(\begin{pmatrix} x + 4 \\ y - 5 \end{pmatrix} = \begin{pmatrix} 2 \\ -3 \end{pmatrix}\).

Equating the components, we get:

\(x + 4 = 2\) and \(y - 5 = -3\).

Solving for \(x\) and \(y\):

\(x = 2 - 4 = -2\)

\(y = -3 + 5 = 2\)

Therefore, the coordinates of B are \((-2, 2)\).