  In this paper we discuss $SU(5)^{3}$ with cyclic symmetry as a possible grand
unified theory (GUT). The basic idea of such a tri-unification is that there is
a separate $SU(5)$ for each fermion family, with the light Higgs doublet(s)
arising from the third family $SU(5)$, providing a basis for charged fermion
mass hierarchies. $SU(5)^{3}$ tri-unification reconciles the idea of gauge
non-universality with the idea of gauge coupling unification, opening the
possibility to build consistent non-universal descriptions of Nature that are
valid all the way up to the scale of grand unification. As a concrete example,
we propose a grand unified embedding of the tri-hypercharge model $U(1)_Y^3$
based on an $SU(5)^{3}$ framework with cyclic symmetry. We discuss a minimal
tri-hypercharge example which can account for all the quark and lepton
(including neutrino) masses and mixing parameters. We show that it is possible
to unify the many gauge couplings into a single gauge coupling associated with
the cyclic $SU(5)^{3}$ gauge group, by assuming minimal multiplet splitting,
together with a set of relatively light colour octet scalars. We also study
proton decay in this example, and present the predictions for the proton
lifetime in the dominant $e^+\pi^0$ channel.
