  The phase diagram of the $\mathbb{Z}(5)$ spin model is studied numerically on
the square lattice by means of the {\sl Density Matrix Renormalization Group}.
In the regime where the two nearest-neighbor couplings have opposite signs, a
critical phase, not observed in earlier Monte Carlo simulations, is identified.
The new phase diagram is in agreement with predictions made by M. den Nijs
[{\sl Phys. Rev. B} {\bf 31}, 266 (1985)] but for the $\mathbb{Z}(7)$ model
rather than the $\mathbb{Z}(5)$ one. All critical phases are shown to be
compatible with a central charge $c=1$. The magnetization scaling dimension
displays however a different behavior in the different critical phases.
