  We study N=(m,0) super-Poincare invariant six-dimensional massless and
five-dimensional massive on-shell amplitudes. We demonstrate that in six
dimensions, all possible three-point amplitudes involving tensor multiplets are
necessarily embedded in gravitational theories. For non-gravitational
amplitudes we consider instead five-dimensional massive amplitudes with N=(2,0)
supersymmetry, aiming at describing the world volume theory of multiple M5
branes compactified on M^{4,1}x S^1. We find non-gravitational amplitudes whose
on-shell degrees of freedom are shown to match those of the massive particle
states that arise from self-dual strings wrapping a circle. Along the way we
find interesting hints of a fermionic symmetry in the (2,0) theory, which
accompanies the self-dual tensor gauge symmetry. We also discuss novel theories
with (3,0) and (4,0) supersymmetry.
