  We calculate non-singlet quark operator matrix elements of deep-inelastic
scattering in the chiral limit including operators with total derivatives. This
extends previous calculations with zero-momentum transfer through the operator
vertex which provides the well-known anomalous dimensions for the evolution of
parton distributions, as well as calculations in off-forward kinematics
utilizing conformal symmetry. Non-vanishing momentum-flow through the operator
vertex leads to mixing with total derivative operators under renormalization.
In the limit of a large number of quark flavors $n_f$ and for low moments in
full QCD, we determine the anomalous dimension matrix to fifth order in the
perturbative expansion in the strong coupling $\alpha_s$ in the
$\overline{\mbox{MS}}$-scheme. We exploit consistency relations for the
anomalous dimension matrix which follow from the renormalization structure of
the operators, combined with a direct calculation of the relevant diagrams up
to fourth order.
