  Two renormalization group invariant quantities in quantum chromodinamics
(QCD), defined in Euclidean space,namely, Adler D-function of electron-positron
annihilation to hadrons and Bjorken polarized deep-inelastic scattering sum
rule, are considered. It is shown, that the 5-th order corrections to them in
$\overline{MS}$-like renormalization prescriptions, proportional to Riemann
$\zeta$-function $\zeta\left(4\right)$, can be restored by the transition to
the C-scheme, with the $\beta$-function, analogous to Novikov, Shifman,
Vainshtein and Zakharov exact $\beta$-function in $\mathcal{N}=1$
supersymmetric gauge theories. The general analytical expression for these
corrections in $SU\left(N_c\right)$ QCD is deduced and their scale invariance
is shown. The $\beta$-expansion procedure for these contributions is performed
and mutual cancellation of them in the 5-th order of the generalized Crewther
identity are discussed.
