This paper presents a detailed account of evaluation of the electron anomalous magnetic moment a_e which arises from the gauge-invariant set, called Set V, consisting of 6354 tenth-order Feynman diagrams without closed lepton loops. The latest value of the sum of Set V diagrams evaluated by the Monte-Carlo integration routine VEGAS is 8.726(336)(alpha/pi)^5, which replaces the very preliminary value reported in 2012. Combining it with other 6318 tenth-order diagrams published previously we obtain 7.795(336)(alpha/pi)^5 as the complete mass-independent tenth-order term. Together with the improved value of the eighth-order term this leads to a_e(theory)=1 159 652 181.643(25)(23)(16)(763) times 10^{-12}, where first three uncertainties are from the eighth-order term, tenth-order term, and hadronic and elecroweak terms. The fourth and largest uncertainty is from alpha^{-1}=137.035 999 049(90), the fine-structure constant derived from the rubidium recoil measurement. Thus, a_e(experiment) - a_e(theory)= -0.91(0.82) times 10^{-12}. Assuming the validity of the standard model, we obtain the fine-structure constant alpha^{-1}(a_e)=137.035 999 1570(29)(27)(18)(331), where uncertainties are from the eighth-order term, tenth-order term, hadronic and electroweak terms, and the measurement of a_e. This is the most precise value of alpha available at present and provides a stringent constraint on possible theories beyond the standard model.
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