  We show that when the supersymmetric SU(5) model is extended to explain small
neutrino masses by the type III seesaw mechanism, the new {\bf 24}-dimensional
fields needed for the purpose can act as messengers for transmitting SUSY
breaking from a hidden sector to the visible sector. For the three {\bf 24}
case, the constraints of grand unification and suppressed lepton flavor
violation restrict the seesaw scale in this case to be in the narrow range of
$10^{12}-10^{13}$ GeV. The model predicts (i) a stable LSP gravitino with mass
in the range of 1-10 MeV which can be a cold dark matter of the universe; (ii)
a stau NLSP which is detectable at LHC; (iii) a lower bound on the branching
ratio $BR(\mu \to e \gamma)$ larger than $10^{-14}$ testable by the ongoing MEG
experiment as well as characteristic particle spectrum different from other
SUSY breaking scenarios. We also discuss the case with two {\bf 24} fields,
which is the minimal case that can explain neutrino oscillation data.
