  We consider five-dimensional massive vector-gravity theory which is based on
the foliation preserving diffeomorphism and anisotropic conformal invariance.
It does not have an intrinsic scale and the only relevant parameter is the
anisotropic factor $z$ which characterizes the degree of anisotropy between the
four-dimensional spacetime and the extra dimension. We assume that physical
scale $M_*$ emerges as a consequence of spontaneous conformal symmetry breaking
of vacuum solution. It is demonstrated that a very small mass for the vector
particle compared to $M_*$ can be achieved with a relatively mild adjustment of
the parameter $z$. At the same time, it is also observed that the motion along
the extra dimension can be highly suppressed and the five-dimensional theory
can be effectively reduced to four-dimensional spacetime.
