In triangle \(ABC\), point \(D\) lies on side \(BC\) such that \(BD = 2\) and \(DC = 3\). The coordinates of \(A\) are \((2, 5)\), and the coordinates of \(B\) and \(C\) are \((0, 0)\) and \((5, 0)\), respectively. Find the area of triangle \(ABD\). Let's think step by step and output the final answer within \boxed{}.
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