  We propose an SU(5) grand unified model with an invisible axion and the
unification of the three coupling constants which is in agreement with the
values, at $M_Z$, of $\alpha$, $\alpha_s$, and $\sin^2\theta_W$. A discrete,
anomalous, $Z_{13}$ symmetry implies that the Peccei-Quinn symmetry is an
automatic symmetry of the classical Lagrangian protecting, at the same time,
the invisible axion against possible semi-classical gravity effects. Although
the unification scale is of the order of the Peccei-Quinn scale the proton is
stabilized by the fact that in this model the standard model fields form the
SU(5) multiplets completed by new exotic fields and, also, because it is
protected by the $Z_{13}$ symmetry.
