  The highest exclusive jet multiplicity studied at LEP experiments is five. In
this paper we compute the next-to-leading order QCD corrections to e+e-
annihilation to five jets, essentially closing the (pure) perturbative QCD
studies of exclusive jetty final states at LEP. We compare fixed-order
perturbative results with ALEPH data. We estimate hadronization corrections to
five-jet observables using the event generator SHERPA, which employs the CKKW
procedure to combine a reliable perturbative treatment of high-multiplicity jet
final states with parton showers. We show that a competitive value of the
strong coupling constant alpha_s(M_Z) = 0.1156 +0.0041 -0.0034 can be extracted
from the distribution of the five-jet resolution parameter and the five-jet
rate at LEP1 and LEP2.
