We present the first genuine QCD five-loop calculation
of the vacuum polarization functions: analytical
terms of order alpha_s^4 n_f^2 to the
absorptive parts of vector and scalar correlators.
These corrections form an important gauge-invariant
subset of the full O(alpha_s^4) correction to
$e^+ e^- annihilation into hadrons and the Higgs decay rate
into hadrons respectively. They discriminate between different
widely used estimates of the full result.