  The effective Higgs theories at the TeV scale in supersymmetric $SU(5)$ grand
unification models are systematically derived. Restricted to extensions on
$\mathbf{5}_{H}$ containing the Higgs sector we show that only two types of
real (vector-like) models and one type of chiral model are found to be
consistent with perturbative grand unification. While the chiral model has been
excluded by the LHC data, the fate of perturbative unification will be uniquely
determined by the two classes of vector-like models.
