Step Up Converter (Boost) is Wasting too much Power
Assuming that the figure for the converter efficiency is 85% that means when it is asked to deliver a 5W output (10V @ 0.5A) that the input power requirement is:


  Input Power = Output Power / 0.85 = 5W / 0.85 = 5.88W


At a 5V output of the power bank that would equate to 5.88W / 5V = 1.18A

In the past I did some testing of power banks and USB charging cables and found that there was a considerable voltage drop at the output of the cable due to the both the voltage drop in the cable and the power bank output not staying at 5V when under load. 

If we take your measured value of input current as a good reading (2.7A) it implies that the voltage feeding the boost converter is:


  Voltage = Input Power / 2.7A = 5.88W / 2.7A = 2.17V


I encourage you to take a measurement of the actual voltage at the input of the boost converter. It is highly likely that it is not the 5V that you think it is. 

It is also possible that the stated efficiency of the converter is not 85%. It could be way lower if the load on the converter was lower than its full rated capacity or if it is a cheap piece of junk with pretend specifications.