We propose a model based on $SU(5) \times { }^{(d)}T$ which successfully gives rise to near tri-bimaximal leptonic mixing as well as realistic CKM matrix elements for the quarks. The Georgi-Jarlskog relations for three generations are also obtained. There are only nine operators allowed in the Yukawa sector up to at least mass dimension seven due to an additional $Z_{12} \times Z'_{12}$ symmetry, which also forbids, up to some high orders, operators that lead to proton decay. The resulting model has a total of nine parameters in the charged fermion and neutrino sectors, and hence is very predictive. In addition to the prediction for $\theta_{13} \sim \theta_{c}/3 \sqrt{2}$, the model gives rise to a sum rule, $\tan^{2}\theta_{\odot} \simeq \tan^{2} \theta_{\odot, \mathrm{TBM}} - \frac{1}{2} \theta_{c} \cos\beta$, which is a consequence of the Georgi-Jarlskog relations in the quark sector. This deviation could account for the difference between the experimental best fit value for the solar mixing angle and the value predicted by the tri-bimaximal mixing matrix.