It was a good attempt, but you missed some things.
The big one is that if your Arduino is connected to the power bank too, it will draw some current, and quite a lot of it too. One of the moderators Nick Gammon has written an article (linked in the "Useful links" sticky) about this, and found that an Uno draws about 50 mA in normal use, no matter what sketch is uploaded. That brings the estimated operating time down to 208 hrs.
The next thing was mentioned by MarkT. 10,400 mAh is very likely the sum of the batteries' capacities. Even a 100% efficient boost converter will derate that capacity by 3.6/5, giving a 150 hr estimated operating time.
This estimate needs to be further reduced to account for inefficiency in the boost conversion and the quiescent current of the conversion circuit. There's too much uncertainty about that to calculate it from first principles though, and probably won't make that much of a difference anyway, so lets just leave 150 hrs. as a pie-in-the-sky ideal maximum.
So we went from almost 5 years estimate to less than a week. Successfully running an Arduino project from a battery is much more difficult than just finding a power source capable of producing 5V. As you can see from this calculation, with a normal sketch your battery life is horrible even with a pretty chunky bank. If you want to get anything resembling good battery life, you need to get off a development board and start using ATmega chip barebones. That way you can use the substantial power reduction and sleeping features of the chip to potentially reduce the current consumption by hundreds of times.
These things may require substantial rewrites of your code though. If you are using large amounts of delay(), it will be very difficult to properly work in the different sleep modes and get a large amount of power saving.