  Present work deals with the two fluid Bianchi Type-V cosmological models
consisting of matter and radiating source in the $f(R, T)$ theory of gravity
studied by Harko et al. (2011). In this paper, we developed a new idea about
$f(R, T)$ gravity with the help of two fluids: one fluid is matter field
modeling material content of the Universe and other fluid is radiation field
modeling the CMB. We have determined the solution of the two fluid
gravitational field equations with the systematic structure in $f(R, T)$
gravity. Here we have deliberated four types of universe such as dust universe,
radiation universe, hard universe and Zeldovich universe and also extended our
work to observe the big rip and big bang singularity. We have also tested the
cosmological parameters.
