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We extend the recently proposed $SU(5) \times \mathcal{T}_{13}$ model for theasymmetric texture to the up-type quark and seesaw sectors. The hierarchicalup-type quark masses are generated from higher-dimensional operators involvingfamily-singlet Higgses, gauge-singlet familons, and vectorlike messengers. Thecomplex-tribimaximal (TBM) seesaw mixing arises from the vacuum structure of aminimal number of familons, resulting in an alignment between the Yukawa andMajorana matrices of the seesaw formula. Introducing four right-handedneutrinos, normal ordering of the light neutrino masses is obtained, with$m_{\nu_1} = 27.6\ \mathrm{meV}$, $m_{\nu_2} = 28.9\ \mathrm{meV}$ and$m_{\nu_3} = 57.8\ \mathrm{meV}$. Their sum almost saturates Planck'scosmological upper bound ($120$ $\text{meV}$). The right-handed neutrino massesare expressed in terms of two parameters for a particular choice of familonvacuum alignment. We predict the $\require{cancel}\cancel{CP}$Jarlskog-Greenberg invariant to be $|\mathcal{J}| = 0.028$, consistent with thecurrent PDG estimate, and Majorana invariants $|\mathcal{I}_1| = 0.106$ and$|\mathcal{I}_2| = 0.011$. A sign ambiguity in the model parameters leads totwo possibilities for the invariant mass parameter $|m_{\beta \beta}|$: $13.02$or $25.21$ $\text{meV}$, both within an order of magnitude of the most rigorousexperimental upper limit ($61$--$165$ $\text{meV}$).

Tribimaximal Mixing in the $SU(5) \times \mathcal{T}_{13}$ Texture