We report the results of the first complete QCD five-loop
calculation, viz. analytical contribution of order m_q^2 alpha_s^4,
to the (absorptive part of) the vacuum polarization function. The
contribution directly leads to the knowledge of the the
full O( \als^4 m_q^2/ s)correction to the total cross-section
of e^+ e^- annihilation into hadrons. We compare
our results with predictions following from various optimization
schemes.