  In DBI inflation the cubic action is a particular linear combination of the
two, otherwise independent, cubic operators \dot \pi^3 and \dot \pi (\partial_i
\pi)^2. We show that in the Effective Field Theory (EFT) of inflation this is a
consequence of an approximate 5D Poincar\'e symmetry, ISO(4,1), non-linearly
realized by the Goldstone \pi. This symmetry uniquely fixes, at lowest order in
derivatives, all correlation functions in terms of the speed of sound c_s. In
the limit c_s \to 1, the ISO(4,1) symmetry reduces to the Galilean symmetry
acting on \pi. On the other hand, we point out that the non-linear realization
of SO(4,2), the isometry group of 5D AdS space, does not fix the cubic action
in terms of c_s.
