  We investigate the inflationary cosmology involving an SU(5) GUT (grand
unified theory) singlet scalar with non-minimal coupling to the Ricci scalar.
In this scenario the scale of grand unification is set by the inflaton vev when
the inflaton rolls down its potential towards its minimum $v$, thereby relating
inflationary dynamics to GUT symmetry breaking with a prediction $r \simeq
0.025$ for the tensor-to-scalar ratio to be tested by the next generation CMB
experiments. We show in this inflationary framework involving inflection-point
how a suitable choice of parameters in $SU(5)$ leads to a bump in the scalar
power spectrum with production of Primordial Blackholes (PBH) of masses
$10^{17}-10^{18}$g ($ 10 - 100 M_\odot$). We derive the constraints on the self
quartic and mixed quartic couplings of the inflaton in SU(5) that are
consistent with the inflationary analysis. Moreover, we also show that this
scenario leads to large amplitude induced second-order tensor perturbations
propagating as Gravitational Waves (GW) with amplitude $\Omega_{\rm GW}h^2 \sim
10^{-17}$ and peak frequency $f_{\rm peak} \sim$ (0.1 - 1) Hz, which can be
detected in the next generation GW observatories like LISA, BBO, ET, etc. Thus,
we unify the $SU(5)$ framework with PBH via inflection-point inflation showing
how the upcoming measurements of PBH and GW will enable us to probe the scale
of $SU(5)$ symmetry breaking, and thereby complementing the laboratory based
experiments. We also discuss scenarios involving the Pati-Salam and
Trinification gauge groups and its impact on quartic and mixed-quartic
couplings that may lead to PBH and detectable GW signals.
