Transverse momentum, $p_T$, spectra are of prime importance in order to extract crucial information about the evolution dynamics of the system of particles produced in the collider experiments. In this work, the transverse momentum spectra of charged hadrons produced in $PbPb$ collision at $5.02$ TeV have been analyzed using different distribution functions in order to gain strong insight into the information that can be extracted from the spectra. We have also discussed the applicability of the unified statistical framework on the spectra of charged hadron at $5.02$ TeV