We have evaluated the eighth-order contribution to the anomalous magnetic moment of the electron arising from the 518 vertex diagrams which have no closed electron loops. Our result is -1.934(137)(±)4. The theoretical error represents the estimated accuracy (90% confidence limit) of the required numerical integration. Combining this with the updated results of the previous four papers in this series, we find the complete eighth-order QED contribution to be -1.434(138)(±)4. If one uses, for ±-1, the value 137.035 997 9(32) obtained from the quantized Hall effect, this leads to the most accurate theoretical value available at present for the magnetic moment anomaly of the electron, aeth=1159652140(28)×10-12, which is within 1.7 standard deviations of the experimental values for the electron and positron: ae-expt=1159652188.4(4.3)×10-12, ae+expt=1159652187.9(4.3)×10-12.