  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 K\'ara, P\'or, and
Wood [\emph{Discrete Comput. Geom.} 34(3):497--506, 2005].
