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)