  We investigate how the speed of propagation of physical excitations is
encoded in the coefficients of five-point interactions. This leads to a
superluminality bound on scalar five-point interactions, which we present here
for the first time. To substantiate our result, we also consider the case of
four-point interactions for which bounds from S-matrix sum rules exist and show
that these are parametrically equivalent to the bounds obtained within our
analysis. Finally, we extend the discussion to a class of higher-point
interactions.
