DiracSubstitute5[exp] rewrites \gamma^5 in terms of the chirality projectors \gamma^6 and \gamma^7. DiracSubstitute5 is also an option of various FeynCalc functions that handle Dirac algebra.
Overview, DiracSubstitute67, DiracGamma, ToDiracGamma67.
GA[5]
DiracSubstitute5[%]\bar{\gamma }^5
\bar{\gamma }^6-\bar{\gamma }^7
SpinorUBar[Subscript[p, 1]] . GA[\[Mu]] . GA[5] . GA[\[Nu]] . SpinorU[Subscript[p, 2]]
DiracSubstitute5[%]\bar{u}\left(p_1\right).\bar{\gamma }^{\mu }.\bar{\gamma }^5.\bar{\gamma }^{\nu }.u\left(p_2\right)
\left(\varphi (\overline{p}_1)\right).\bar{\gamma }^{\mu }.\left(\bar{\gamma }^6-\bar{\gamma }^7\right).\bar{\gamma }^{\nu }.\left(\varphi (\overline{p}_2)\right)