TTP10-14 R(s), Bjorken sum rule and the Crewther Relation in order alpha_s^4

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.