Measuring a 18650 cell
Yes, that would be correct if the DC-DC converter was 100% efficient. Maybe it's 80% efficient, so it would be more like 4000mAh @ 5V. 
If my 80% number is reasonable, it's more like 2400mAh, which is fairly decent. The number will vary with the current draw (it will be lower at very low and very high currents). 
It's not easy to estimate the efficiency of the converter in your power bank. If you use 80% and it's a good quality power bank you'll probably be close. An electronic load with appropriate features for battery testing is the proper way to test battery capacity- you can test with constant current, constant power or resistance type loading and set a safe cutoff voltage at which to terminate the test. 


Markings on the batteries, as Chris says, can be exaggerated a bit or they can be extreme lies (like 10% of the claimed capacity- 500 or 600mAh). Especially those procured through dubious channels. If they're willing to lie about the package contents to illegally airmail it, they're more than willing to lie about the battery capacity.