  We study the possible correspondence between 5-dimensional primordial black
holes and massive 5-dimensional KK gravitons as dark matter candidate within
the recently proposed dark dimension scenario that addresses the cosmological
hierarchy problem. First, we show that in the local universe a population of
5-dimensional black holes with $M_{\rm BH}\sim 7\times 10^{13}~{\rm g}$ would
be practically indistinguishable from a KK tower of dark gravitons with $m_{\rm
DM} \sim 50~{\rm keV}$. Second, we connect the mass increase of 5-dimensional
black holes and the related temperature decrease with the cooling of the tower
of massive spin-2 KK excitations of the graviton. The dark gravitons are
produced at a mass $\sim 1 - 50~{\rm GeV}$ and the bulk of their mass shifts
down to roughly $1 - 100~{\rm keV}$ today. The cooling of the system proceeds
via decay to lighter gravitons without losing much total mass density,
resembling the intra-tower decays that characterize the cosmological evolution
of the dynamical dark matter framework. We associate the intra-tower decays of
the graviton gas with the black hole growth through accretion. We also discuss
that the primordial black hole $\leftrightharpoons$ dark graviton gas
connection can be nicely explained by the bound state picture of black holes in
terms of gravitons.
