  We calculate the shape dependence of entanglement entropy in
(5+1)-dimensional conformal field theory in terms of the extrinsic curvature of
the entangling surface, the opening angles of possible conical singularities,
and the conformal anomaly coefficients, which are required to obey a single
constraint. An important special case of this result is given by the
interacting (2,0) theory describing a large number of coincident M5-branes. To
derive the more general result we rely crucially on the holographic
prescription for calculating entanglement entropy using Lovelock gravity. We
test the conjecture by relating the entanglement entropy of the free massless
(1,0) hypermultiplet in (5+1)-dimensions to the entanglement entropy of the
free massive chiral multiplet in (2+1)-dimensions, which we calculate
numerically using lattice techniques. We also present a numerical calculation
of the (2+1)-dimensional renormalized entanglement entropy for the free massive
Dirac fermion, which is shown to be consistent with the F-theorem.
