Embedding Phenomenological Quark-Lepton Mass Matrices into SU(5) Gauge Models

We construct phenomenological quark-lepton mass matrices based on S$_3$ permutation symmetry in a manner fully compatible with SU(5) grand unification. The Higgs particles we need are {\bf 5}, {\bf 45} and their conjugates. The model gives a charge $-$1/3 quark vs charged lepton mass relation, and also a good fit to mass-mixing relations for the quark sector, as well as an attractive mixing pattern for the lepton sector, explaining a large mixing angle between $\nu_\mu$ and $\nu_\tau$, and either large or small $\nu_e-\nu_\mu$ mixing angle, depending on the choice of couplings, consistent with the currently accepted solutions to the solar neutrino problem.