We propose an adjoint SU(5) GUT model with a T-7 family symmetry and an extra Z(2) circle times Z(3) circle times Z(4). Z'(4) circle times Z(12) discrete group that successfully describes the prevailing Standard Model fermion mass and mixing pattern. The observed hierarchy of the charged fermion masses and the quark mixing angles arises from the Z(3)circle times Z(4)circle times Z(12) symmetry breaking, which occurs near the GUT scale. The light active neutrino masses are generated by type-I and type-III seesaw mechanisms mediated by the fermionic SU(5) singlet and the adjoint 24-plet. The model predicts the effective Majorana neutrino mass parameter of neutrinoless double beta decay to be m(beta beta)= 4 and 50 meV for the normal and the inverted neutrino spectra, respectively. We construct several benchmark scenarios, which lead to SU(5) gauge coupling unification and are compatible with the known phenomenological constraints originating from the lightness of neutrinos, proton decay, dark matter, etc. These scenarios contain TeV-scale colored fields, which could give rise to a visible signal or be stringently constrained at the LHC.