  The article by Anton E. M. van de Ven, Class. Quantum Grav. \textbf{15}
(1998), is one of the fundamental references for higher-order heat kernel
coefficients in curved backgrounds and with non-abelian gauge connections. In
this manuscript, we point out two errors and ambiguities in the $\mathsf{a}_5$
coefficient, which may also affect the higher-order ones.
