  It is well known that the minimal renormalizable $SU(5)$ grand unified theory
is ruled out: it predicts same masses of down quarks and charged leptons, the
gauge couplings do not unify and neutrinos are massless. We show here that all
this can be cured simultaneously by the addition of higher-dimensional
effective operators. However, the theory lives on the edge since the
unification scale turns out as low as roughly $10^{14}\,$GeV, threatening
proton longevity. If the lower bound on the proton lifetime was to be increased
by an order of magnitude, the usual desert in energies between the weak and
unification scales would be populated. We also revisit two minimal extensions
of this theory that offer a dynamical seesaw origin of neutrino mass, and
discuss the resulting consequences.
