  Chiral perturbation theory describes the low energy dynamics of mesons and
baryons in terms of the nonlinear Goldstone boson and fermion degrees of
freedom. Through the Young tensor technique, we construct the on-shell operator
bases for the meson-baryon system up to $p^5$-order, using the chiral dimension
power counting and heavy baryon expansion. For the Lorentz structure,
additional treatments on off-shell external sources and operators with higher
derivatives are necessarily considered, while for the internal structure, the
invariant tensor basis is converted into the trace basis equivalently, and
Cayley-Hamilton relations are utilized to classify different CP
eigen-operators. Finally we present the complete operator set of $C$+$P$+,
$C$+$P$-, $C$-$P$+, and $C$-$P$- eigen-operators at the $p^5$-order, and obtain
the operator counting from the Hilbert series.
