We give a short presentation of the first genuine QCD five-loop calculations, viz. analytical contributions of order alpha(s)(4)n(f)(2) and m(q)(2)alpha(s)(4)n(f)(2) to the vacuum polarization function of vector currents. These corrections form an important gauge-invariant subset of the full O(alpha(s)(4)) correction to e(+)e(-) annihilation into hadrons.