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We have examined whether a non-renormalizable field theory can have a non-trivial fixed point. As a simple example, SU(2) pure Yang-Mills theory in five dimensions is considered with a lattice regularization. Taking into account both fundamental and adjoint representations, we search for a non-trivial second-order phase transition by- Monte Carlo techniques. Along the phase boundary for deconfining phase transition, energy discontinuities of by hysteresis curves tend to diminish as the coupling constant for adjoint representation decreases to large negative values

On Existence of Non-Renormalizable Field Theory: Pure SU(2) Lattice Gauge Theory in Five Dimensions