5. As shown in the figure, in isosceles trapezoid $ABCD$, $AB \parallel DC, AB=998, DC=1001, AD=1999$, point $P$ is on line segment $AD$. Then the number of points $P$ that satisfy the condition $\angle APC = 90^{\circ}$ is ( ).
(A) 0
(B) 1
(C) 2
(D) an integer not less than 3
5. (C)
The midpoint $M$ of $A D$ subtends a $90^{\circ}$ angle with $B C$; also, let $N$ be a point on $A D$ such that $A N: N D=998: 1001$. From the fact that $\triangle A B N$ and $\triangle D C N$ are both isosceles triangles, it follows that $N$ subtends a $90^{\circ}$ angle with $B C$. Noting that the circle with $B C$ as its diameter intersects $A D$ at most at two points, the number of points sought is 2.