Signatures of quark-lepton unification can be experimentally verified by rare-kaon-decay processes provided the SU(4)/sub C/-breaking scale M/sub C//similar to/10/sup 5/--10/sup 6/ GeV. With the single intermediate symmetry, SU(2)/sub L/ x U(1)/sub R/ x SU(4)/sub C/ in SO(10), we find, for the first time, that such a scale and small Majorana neutrino masses are allowed when gravity-induced corrections due to a five-dimensional operator, arising out of spontaneous compactification of extra dimensions, are included. For such lower values of M/sub C/, the predicted proton lifetime is large depending upon the value of sin/sup 2/theta/sub W/ in the range 0.22--0.24. For still larger values of M/sub C/, neutrino masses and proton lifetime decrease, and the latter saturates the Irvine-Michigan-Brookhaven limit when M/sub C//similar to/10/sup 11/--10/sup 12/ GeV.