I tested twice. This battery has a max of 3000mAh (probably less). It took my 5000mAh phone battery from 15% to 72%.
They have to know they are misleading us with the 5000 mAh claim. Very disappointing.
-- Update: To make matters worse, even though I have returned the charger and was told I was getting a full refund, Anker customer service is offering me $4 instead of a full refund (even though I've already returned it).
They explained their deceptive advertising: "And in regards to efficiency, all our PowerCores burn 30-40% of their power when they are charging other devices. So the Anker 321 wireless battery has 5,000mah of power, but the power left for charging your device is in fact 3,000 - 3500mah."
It would be like a car maker saying "We get 100mpg" and when you find it doesn't, they explain "That's when we're towing it downhill." Ridiculous and unacceptable.