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Abstract We focus on a non-abelian gauge field coupled to a single (but general) representation of a family of N f fermions. By using the same machinery that had allowed us to evaluate the sub-leading large-N f term of the five-loop Beta function earlier, we here report on a confirmation of the all-N f result that has in the meantime been published by another group. Furthermore, in order to push forward the 5-loop renormalization program regarding gauge parameter dependence, we present the linear terms of the complete set of anomalous dimensions, in an expansion in the covariant gauge parameter around the Feynman gauge.