Every large point set contains many collinear points or an empty pentagon

We prove the following generalised empty pentagon theorem: for every integer l 2, every sufficiently large set of points in the plane contains ̀ collinear points or an empty pentagon. As an application, we settle the next open case of the "big line or big clique" conjecture of Kára, Pór, and Wood [Discrete Comput. Geom. 34(3):497-506, 2005]