  Interest in cosmological singularities has remarkably grown in recent times,
particularly on future singularities with the discovery of late-time
acceleration of the universe and dark energy. Recent work has seen a proper
classification of such singularities into strong and weak based on their
strength, with weak singularities being the likes of sudden, w and big freeze
singularities and strong singularities like the big rip. This has led to a
classification of such singularities in various types like Big rip is Type 1,
w-singularity is type V etc. While singularities of type I-type IV have been
discussed vividly by taking into account inhomogeneous equations of state
(EOS), the same has not been attempted for type V singularities. So in this
work we have discussed in detail about the formation of type V singularities in
various cosmologies after considering inhomogeneous equations of state. We
consider two inhomogeneous forms of the EOS in the context of four different
cosmological backgrounds ; standard general relativistic cosmology, an
asymptotically safe cosmology, a cosmology inspired by modified area-entropy
relations, generalized uncertainty principles, holographic renormalization and
Chern-Simons gravity( all of which can be coincidentally described by the same
form of the modified Friedmann equation) and an f(R) gravity cosmology. We show
in detail that one sees some very big differences in the occurence conditions
of type V singularities when one makes such considerations. In the particular
case of the f(R) gravity cosmology, we see that the type V singularities get
completely removed. This work goes to show that the creation and formation of
type V singularities is influenced most strongly by the form of the equation of
state that one considers, way more so than what background cosmology one
chooses.
