  We present the first determination of Higgs-boson decay to hadrons at the
next-to-next-to-next-to-next-to-leading order of perturbative QCD in the limit
of a heavy top quark and massless light flavours. This result has been obtained
by computing the absorptive parts of the relevant five-loop self-energy for a
general gauge group and combining the outcome with the corresponding
coefficient function already known to this order in QCD. Our new result reduces
the uncertainty due to the truncation of the perturbation series to a fraction
of the uncertainty due to the present error of the strong coupling constant. We
have also performed the corresponding but technically simpler computations for
direct Higgs decay to bottom quarks and for the electromagnetic R-ratio in e^+
e^- -> hadrons, thus verifying important fifth-order results obtained so far
only by one group.
