Realistic fermion masses and nucleon decay rates in supersymmetric SU(5) with vectorlike matter

We show that by adding a vectorlike $5+\overline{5}$ pair of matter fields to the spectrum of the minimal renormalizable supersymmetric $SU(5)$ theory the wrong relations for fermion masses can be corrected, while being predictive and consistent with proton lifetime limits. Threshold correction from the vectorlike fields improves the unification of gauge couplings compared to the minimal model. It is found that for supersymmetric spectra lighter than 3 TeV, which would be testable at the LHC, at least some of the nucleon decay modes should have partial lifetimes shorter than about $2\times {10}^{34}$ years, which is within reach of ongoing and proposed experiments.