5. On the plane, there are two points $P$ and $Q$. The number of triangles that can be drawn with $P$ as the circumcenter and $Q$ as the incenter is ( ).
(A) Only 1 can be drawn
(B) 2 can be drawn
(C) At most 3 can be drawn
(D) Infinitely many can be drawn
5.(D).

Draw a circle $\odot P$ such that $Q$ is inside $\odot P$; take any point $A$ on $\odot P$, and let the ray $A Q$ intersect $\odot P$ at $D$; with $D$ as the center and $D Q$ as the radius, draw an arc intersecting $\odot P$ at $B$ and $C$, $\triangle A B C$ is the desired triangle. Since $\odot P$ can be of any size, and point $A$ is taken arbitrarily, there are infinitely many triangles.