  We consider the scenario where all the couplings in the theory are strong at
the cut-off scale, in the context of higher dimensional grand unified field
theories where the unified gauge symmetry is broken by an orbifold
compactification. In this scenario, the non-calculable correction to gauge
unification from unknown ultraviolet physics is naturally suppressed by the
large volume of the extra dimension, and the threshold correction is dominated
by a calculable contribution from Kaluza-Klein towers that gives the values for
\sin^2\theta_w and \alpha_s in good agreement with low-energy data. The
threshold correction is reliably estimated despite the fact that the theory is
strongly coupled at the cut-off scale. A realistic 5d supersymmetric SU(5)
model is presented as an example, where rapid d=6 proton decay is avoided by
putting the first generation matter in the 5d bulk.
