  In this paper we attempt a non-perturbative study of the five dimensional,
anisotropic SU(2) gauge theory on the lattice using Monte-Carlo techniques. Our
goal is the exploration of the phase diagram, define the various phases and the
critical boundary lines. Three phases appear, two of them are continuations of
the Strong and the Weak coupling phases of pure 4d SU(2) to non-zero coupling
$\beta^{'}$ in the fifth transverse direction and they are separated by a
crossover transition, while the third phase is a 5D Coulombic phase. We provide
evidence that the phase transition between the 5D Coulomb phase and the Weak
coupling phase is a second order phase transition. Assuming that this result is
not altered when increasing the lattice volume we give a first estimate of the
associated critical exponents. This opens the possibility for a continuum
effective five dimensional field theory.
