We propose an adjoint SU(5)GUT model with a T7 family symmetry, that successfully describes the prevailing SM fermion mass and mixing pattern. The light active neutrino masses can be generated by type I and type III see saw mechanisms. The model predictions for both quark and lepton sectors are in a very good agreement with the experimental data. The model predicts an effective Majorana neutrino mass, relevant for neutrinoless double beta decay, with values 4 and 50 meV for the normal and the inverted neutrino spectrum, respectively. The model also features CP conservation in neutrino oscillations. In addition we construct some of the simplest standard model extensions of fields, which sucessfully lead to SU(5) gauge coupling unification and are consistent with the smallness of neutrino masses and proton decay limits. We find limits for the seesaw scale in agreement with phenomenological constraints such as cold dark matter. In the set of configurations analyzed, some of the fields, being coloured, could give rise to potential signals at the LHC.