We extend the recently proposed SU (5) × T 13 model for the asymmetric texture to the up-type quark and Seesaw sectors. The hierarchical up-type quark masses are generated from higher-dimensional operators involving family-singlet Higgses, gauge-singlet familons, and vector-like messengers. The complex-Tribimaximal (TBM) Seesaw mixing arises from the vacuum structure of a minimal number of familons, resulting in an alignment between the Yukawa and Majorana matrices of the Seesaw formula. Introducing four right-handed neutrinos, normal ordering of the light neutrino masses is obtained, with m ν1 = 27.6 meV, m ν2 = 28.9 meV and m ν3 = 57.8 meV. Their sum almost saturates Planck's cosmological upper bound (120 meV). The right-handed neutrino masses are expressed in terms of two parameters for a particular choice of familon vacuum alignment. We predict the¨CP Jarlskog-Greenberg invariant to be |J | = 0.028, consistent with the current PDG estimate, and Majorana invariants |I 1 | = 0.106 and |I 2 | = 0.011. A sign ambiguity in the model parameters leads to two possibilities for the invariant mass parameter |m ββ |: 13.02 meV or 25.21 meV, both within an order of magnitude of the most rigorous experimental upper limit (61-165 meV). *