  The discovery of the Higgs boson at the Large Hadron Collider (LHC) has a
great impact on the minimal supersymmetric extension of the Standard Model
(MSSM). In the context of the constrained MSSM (CMSSM) and its extension with
non-universal masses for the MSSM Higgs doublets (NUHM2), sparticles with
masses $ > 1$ TeV are necessary to reproduce the observed Higgs boson mass of
125-126 GeV. On the other hand, there appears to be a significant amount of
discrepancy between the measured muon $g-2$ and the Standard Model prediction.
A successful explanation of this discrepancy in the MSSM requires new
contributions involving relatively light sparticles with masses $ < 1$ TeV. In
this paper, we attempt to accommodate the two conflicting requirements in an
SU(5) inspired extension of the CMSSM. We assign non-universal but flavor blind
soft supersymmetry breaking masses to the scalar components in $\bar 5$ and 10
matter supermultiplets. The two MSSM Higgs doublets in the 5, $\bar5$
representations of SU(5) are also assigned unequal soft mass$^2$ at $M_{GUT}$.
We identify parameter regions which can simultaneously accommodate the observed
Higgs boson mass and the muon $g-2$ data, and which are compatible with other
phenomenological constraints such as neutralino dark matter relic abundance and
rare B-meson decays. Some regions of the allowed parameter space will be
explored at the upgraded LHC and by dark matter direct detection experiments.
