  We present a gauge mediated supersymmetry breaking model having weak SU(2)
triplet, color SU(3) octet and SU(5) 5-plet messengers, that can simultaneously
explain the muon $(g-2)$ data within 1$\sigma$ and the observed Higgs boson
mass of 125 GeV. Gauge coupling unification is nontrivially maintained. Most of
the parameter space satisfying both is accessible to the 14 TeV LHC. The
lighter of the two staus weighs around (100-200) GeV, which can be a potential
target of the ILC.
