  A realistic extension of the minimal $SU(5)$ theory consisting of the
addition of an adjoint fermion is known to predict light real fermion and
scalar weak triplets, potentially accessible at the LHC. These particles, in
addition to playing a key role in gauge coupling unification, have profound
phenomenological implications. The fermion triplet, that through the seesaw
mechanism offers a testable origin of neutrino mass, has been already
extensively discussed. The scalar triplet develops a vacuum expectation value
that modifies the $W$-boson mass. We show that its low-energy effective theory
is remarkably predictive: in the leading approximation, all the relevant
physical processes involving the scalar triplet depend only on its mass and the
deviation from the Standard Model $W$-mass value.
