  Considering massless axial-vector-vector triangle diagram in the conformal
invariant limit and the the results of recent distinguished analytical
calculations of the 5-loop single-fermion loop corrections to the QED
$\beta$-function, we derive the analytical expressions for the
$C_F^4\alpha_s^4$-contributions to the Bjorken polarized and Gross-Llewellyn
Smith sum rule. This visible in future evaluation can shed extra light on the
reliability of the appearance of $\zeta_3$-term in the explicitly known part of
5-loop corrections to the QED $\beta$-function which are proportional to the
conformal invariant set of $C_F^4\alpha_s^4$ -contributions into to the
$e^+e^-$- annihilation Adler function.
