  It was shown recently that the original SU(5) theory of Georgi and Glashow,
augmented with an adjoint fermionic multiplet 24_F, can be made compatible both
with neutrino masses and gauge coupling unification. In particular, the model
predicts that either electroweak-triplet states are light, within the reach of
the Large Hadron Collider (LHC), or proton decay will become accessible at the
next generation of megaton-scale facilities. In this paper, we present the
computation of the correlation function between the electroweak-triplet masses
and the unification scale at the next-to-next-to-leading-order (NNLO). Such an
accuracy on the theory side is necessary in order to settle the convergence of
the perturbative expansion and to match the experimental precision on the
determination of the electroweak gauge couplings at the Z-boson mass scale.
