  This paper describes a computation of a part of the QED contribution to the
electron anomalous magnetic moment that was performed by the author with the
help of a supercomputer. The computed part includes all 5-loop QED Feynman
graphs without lepton loops. The calculation has led to the result
$A_1^{(10)}[\text{no lepton loops}]=6.793(90)$ that is slightly different than
the value $7.668(159)$ presented by T. Aoyama, T. Kinoshita, and M. Nio in
2018. The discrepancy is about $4.8\sigma$. The computation gives the first
independent check for that value. A shift in the fine-structure constant
prediction is revealed in the paper. The developed calculation method is based
on (a) a subtraction procedure for removing all ultraviolet and infrared
divergences in Feynman parametric space before integration; (b) a nonadaptive
Monte Carlo integration that uses the probability density functions that are
constructed for each Feynman graph individually using its combinatorial
structure. The method is described briefly in the paper (with the corresponding
references to the previous papers). The values for the contributions of nine
gauge-invariant classes splitting the whole set are presented in the paper.
Moreover, the whole set of all 5-loop graphs without lepton loops is split into
807 subsets for comparison (in the future) of the calculated values with the
values obtained by another methods. These detailed results are presented in the
supplemental materials. Also, the supplemental materials contain the
contribution values for each of 3213 individual Feynman graphs. An
"oscillating" nature of these values is discussed. Technical details of the
realization are described.
