Triangle \(ABC\) lies in the Cartesian Plane and has an area of 70. The coordinates of \(B\) and \(C\) are \((12,19)\) and \((23,20),\) respectively, and the coordinates of \(A\) are \((p,q).\) The line containing the median to side \(BC\) has slope \(-5.\) Find the largest possible value of \(p+q.\)
(第二十三届AIME1 2005 第10题)