  We discuss the prescription for the Dirac matrix gamma_5 in dimensional
regularization used in most second- and third-order QCD calculations of
collider cross sections. We provide an alternative implementation of this
approach that avoids the use of an explicit form of gamma_5 and of its (anti-)
commutation relations in the most important case of no more than one gamma_5 in
each fermion trace. This treatment is checked by computing the third-order
corrections to the structure functions F_2 and g_1 in charged-current
deep-inelastic scattering with axial-vector couplings to the W-bosons. We
derive the so far unknown third-order helicity-difference splitting function
Delta P_ns^(2)s that contributes to the next-to-next-to-leading order (NNLO)
evolution of the polarized valence quark distribution of the nucleon. This
function is negligible at momentum fractions x >~ 0.3 but relevant at x << 1.
