We propose to generate non-universal gaugino masses in SU(5) Grand Unified Theory (GUT) with the generalized Planck-scale mediation SUSY breaking mechanism, in which the nonuniversality arises from proper wavefunction normalization with lowest component VEVs of various high dimensional representations of the Higgs fields of SU(5) and an unique F-term VEV by the singlet. Different predictions on gaugino mass ratios with respect to widely studied scenarios are given. The gluino-SUGRA-like scenario, where gluinos are much heavier than winos, bino and universal scalar masses, can be easily realized with appropriate combinations of such highrepresentation Higgs fields. With six GUT-scale free parameters in our scenario, we can solve elegantly the tension between mSUGRA and the present experimental results, including the muon g-2, the dark matter (DM) relic density and the direct sparticle search bounds from the LHC. Taking into account the current constraints in our numerical scan, we have the following observations: (i) The large-tan β ( 35) samples with a moderate M 3 (∼ 5 TeV), a small |A 0 /M 3 | ( 0.35) and a small m A ( 4 TeV) are favoured to generate a 125 GeV SM-like Higgs and predict a large muon g-2, while the stop mass and µ parameter, mainly determined by |M 3 | ( M 0 , |M 1 |, |M 2 |), can be about 6 TeV; (ii) The moderate-tan β (35 ∼ 40) samples with a negative M 3 can have a light smuon (250 ∼ 450 GeV) but a heavy stau ( 1 TeV), which predict a large muon g-2 but a small Br(B s → µ + µ − ); (iii) To obtain the right DM relic density, the annihilation mechanisms should be stau exchange, stau coannihilation, chargino coannihilation, slepton annihilation and the combination of two or three of them; (iv) To obtain the right DM relic density, the spin-independent DM-nucleon cross section is typically much smaller than the present limits of XENON1T 2018 and also an order of magnitude lower than the future detection sensitivity of LZ and XENONnT experiments.scale |M 1/2 | should be larger than about 1 TeV (mg 2|M 1/2 | ), and thus the bino-like neutralino is bounded to be higher than about 400 GeV. All the electroweakinos (higgsinos, sleptons, sneutrinos) are all bounded to be heavier than several hundreds of GeV in CMSSM, and hence the SUSY contributions to the muon g-2 cannot be large enough to account for the discrepancy reported by the Brookhaven AGS [3][4][5]. In fact, CMSSM was found to be excluded at 90% confidence level [6] if it is required to account for both the muon g-2 anomaly and the recent LHC constraints on SUSY particles. The neutralino dark matter in CMSSM, which is heavier than several hundreds of GeV, can mainly have four annihilation mechanisms: stau coannihilation, stop coannihilation, A/H funnel, hybrid (note that the 3 h/Z funnel cannot happen and the focus point or χ ± 1 coannihilation is severely constrained by the recent dark matter direct detection limits) [5,7]. We should mention that even if only the DM relic density upper bound is considered in addition to the muon g-2, a glob...