Every Large Point Set contains Many Collinear Points or an Empty Pentagon

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