Boost Voltage from 5V to 19.1 V
It highly depends on the power consumption of your laptop. Suppose its current consumption is around 2-3A, so if u boost a 5v source to 20v/3A then your 5v source must be able to provide 12A (with the assumption of 100% efficiency!). So there's two problems: 1) is the power-bank capable of providing 12A? for most power-banks the answer is NO, most of them provide current up to 2A. 2) is the step-up circuit capable of handling such a high current? you have to search more for this. For example LM2577 is a step-up IC (and its module is also available) providing about 2A.