ListPlot[{Range[1, 5], Range[5, 10]}]
the structure of the data is important to "easily do it"
on the other hand you might combine plots (there may be a few ways to do so) such as:
ListPlot[Range[1,5]
ListPlot[Range[5,10]
Show[%,%%]
(note if your data is very different the dots may not be all shown unless you limit your plot region to an area where both can be visible within the displayable graphics plot result)
so in summary the structure of your data not in the form {{1,2,3},{4,5,6}}
you might try this and see if the data structure is ok:
ListPlot[{data//Flatten,data2//Flatten}]
if not, then you have {x,y} data or something else. ListPlot handles x,y but again the structure of the list needs to be one of the ones ListPlot is ready to accept. restructure your List[].