Trying to combine two power source into a single micro usb output
In principle you could do what you ask using two DC-DC converters each having 5 V input and 2.5 V isolated output, rated at 2.5 W or greater, and connecting the outputs in series. This would give you 5 V at a maximum current slightly less than double the current available from each 5 V source - slightly less because the converters will be less than 100 % efficient. 

However in practice it would almost certainly be cheaper and easier to buy or make a better power bank that can supply 5 V at 1 A - I'm pretty sure most of them can.

Are you sure it's the power bank that is limiting the current available from each output to 0.5 A, rather than the device(s) you are connecting to it that are only drawing 0.5 A?