  The anomalous magnetic moment of the muon is one of the most fundamental
observables. It has been measured experimentally with a very high precision and
on theory side the contributions from perturbative QED have been calculated up
to five-loop level by numerical methods. Contributions to the muon anomalous
magnetic moment from certain diagram classes are also accessible by alternative
methods. In this paper we present the evaluation of contributions to the QED
corrections due to insertions of the vacuum polarization function at five-loop
level.
