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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 thenext open case of the "big line or big clique" conjecture of K\'ara, P\'or, andWood [\emph{Discrete Comput. Geom.} 34(3):497--506, 2005].

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