  We study a realistic SU(5) grand unified model, where a 45 representation of
scalar fields is added to the Georgi-Glashow model in order to realize the
gauge coupling unification and the masses and mixing of quarks and leptons. The
gauge coupling unification together with constraints from proton decay implies
mass splittings in scalar representations. We assume that an SU(2) triplet
component of the 45 scalar, which is called $S_3$ leptoquark, has a TeV-scale
mass, and color-sextet and color-octet ones have masses of the order of $10^6$
GeV. We calculate one-loop beta functions for Yukawa couplings in the model,
and derive the low-energy values of the $S_3$ Yukawa couplings which are
consistent with the grand unification. We provide predictions for lepton-flavor
violation and lepton-flavor-universality violation induced by the $S_3$
leptoquark, and find that current and future experiments have a chance to find
a footprint of our SU(5) model.
