Abstract
We present a realistic supersymmetric $SU(5)$ model combined with a nonanomalous $U(1{)}_{F}$ symmetry. We find a set of $U(1{)}_{F}$ charges which automatically lead to the realistic mass hierarchy and mixing patterns for quarks, leptons, and neutrinos. All gauge anomalies, including the $[U(1{)}_{F}{]}^{3}$ anomaly, are canceled in our model without invoking the Green-Schwarz mechanism or having exotic fields. Proton decay mediated by dimension-5 operators is automatically suppressed in our model, because the scale set by the largest right-handed neutrino mass is much less than the GUT scale.
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