  We present a non-perturbative study of the phase diagram of 5d SU(2)
Yang-Mills theory with one compact extra dimension on the lattice. Assuming at
least a modest scale separation between the cutoff and the compactification
scales leads to an exponential separation between the compactification scale
and the four-dimensional correlation length. While we demonstrate that it is
not possible to take a full five-dimensional continuum limit, this dynamical
generation of scale hierarchy opens up the possibility for us to make limited,
but non-perturbative, predictions about continuum theories whose low-energy
sector is described by an effective 5d Yang-Mills theory.
