  We propose a grand unified SU(5)$\times$U(1)$_X$ model, where the standard
SU(5) grand unified theory is supplemented by minimal seesaw and a right-handed
neutrino dark matter with an introduction of a global $Z_2$-parity. In the
presence of three right-handed neutrinos (RHNs), the model is free from all
gauge and mixed-gravitational anomalies. The SU(5) symmetry is broken into the
Standard Model (SM) gauge group at $M_{\rm GUT} \simeq 4 \times 10^{16}$ GeV in
the standard manner, while the U(1)$_X$ symmetry breaking occurs at the TeV
scale, which generates the TeV-scale mass of the U(1)$_X$ gauge boson
($Z^\prime$ boson) and the three Majorana RHNs. A unique $Z_2$-odd RHN is
stable and serves as the dark matter (DM) in the present Universe, while the
remaining two RHNs work to generate the SM neutrino masses through the minimal
seesaw. We investigate the $Z^\prime$-portal RHN DM scenario in this model
context, and find that the constraints from the DM relic abundance and the
search results for a $Z^\prime$ boson resonance at the Large Hadron Collider
(LHC) are complementary to narrow down the allowed parameter region, which will
be fully covered by the future LHC experiments (for the $Z^\prime$ boson mass
$<$ 5 TeV). We also briefly discuss the successful implementation of
Baryogenesis and cosmological inflation scenarios in the present model.
