  Gay and Kirby introduced the notion of a trisection of a smooth 4-manifold,
which is a decomposition of the 4-manifold into three elementary pieces.
Rubinstein and Tillmann later extended this idea to construct multisections of
piecewise-linear (PL) manifolds in all dimensions. Given a PL manifold $Y$ of
dimension $n$, this is a decomposition of $Y$ into $\lfloor \frac{n}{2} \rfloor
+ 1$ PL submanifolds. We show that every smooth, oriented, compact 5-manifold
admits a smooth trisection compatible with any desired trisection of its
boundary.
