A parabola intersects the \(y\)-axis at \(B(0,5)\), and intersects the \(x\)-axis at \(C(5,0)\) and at \(A(r,0)\), where \(0<r<5.\) The area of \(\triangle ABC\) is \(5\text{ units}^2.\)
If \(D(p,q)\) is the vertex of the parabola, then determine the area of \(\triangle DBC.\)