  We provide the $\bar{\mathrm{MS}}$ factor of the renormalization constant of
the singlet axial-current operator in dimensional regularization at
$\mathcal{O}(\alpha_s^5)$ in perturbative Quantum Chromodynamics (QCD). The
result is obtained from a formula derived using the Adler-Bell-Jackiw equation
in terms of renormalized operators. The required input consists of the complete
four-loop results for operator renormalization constants obtained by explicit
diagrammatic computation in a previous publication.
