We report on our calculation of the order alpha_s^4
contributions to the Bjorken sum rule for polarized electron-nucleon scattering
and to the (non-singlet) part of the cross section for electron-positron
annihilation into hadrons for the case of a generic colour gauge group.
We confirm at the same order a (generalized)
Crewther relation between the Bjorken sum rule and the corresponding Adler function which provides a strong test
of the correctness of our previously obtained results: the ratio R(s) in QCD
and the five-loop beta-function in quenched QED.