  Maximally supersymmetric SO(10) and SU(6) unified theories are constructed on
the orbifold T^2/(Z_2 x Z'_2), with one length scale R_5 taken much larger than
the other, R_6. The effective theory below 1/R_6 is found to be the highly
successful SU(5) theory in 5D with natural doublet-triplet splitting, no proton
decay from operators of dimension four or five, unified mass relations for
heavier generations only, and a precise prediction for gauge coupling
unification. A more unified gauge symmetry, and the possibility of Higgs
doublets being components of the higher dimensional gauge multiplet, are
therefore compatible with a large energy interval where physics is described by
SU(5) gauge symmetry in 5D. This leads to the distinctive branching ratios for
proton decay from SU(5) gauge boson exchange, p -> l^+ pi^0, l^+ K^0, \bar{nu}
pi^+, \bar{nu} K^+ (l = e, mu), for well-motivated locations for matter.
Several phenomenological features of the higher unified gauge symmetry are
discussed, including the role of an extra U(1) gauge symmetry, which survives
compactification, in the generation of neutrino masses.
