  An empty pentagon in a point set P in the plane is a set of five points in P
in strictly convex position with no other point of P in their convex hull. We
prove that every finite set of at least 328k^2 points in the plane contains an
empty pentagon or k collinear points. This is optimal up to a constant factor
since the (k-1)x(k-1) grid contains no empty pentagon and no k collinear
points. The previous best known bound was doubly exponential.
