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Here is another approach:

data = RandomReal[1, {10, 5}];
dataNorm=Accumulate@Normalize[#,Total]&/@ data;
setLength=Length@data[[1]];
colors = <|1->Red,2->Blue,3->Green,4->Orange,5->Purple|>;

ListPlot[Transpose@dataNorm
        ,Joined->True
        ,Filling -> Table[i -> {{i-1}/.{0}-> 0, colors[i]} ,{i,setLength}]
        ,DataRange-> {0,1}
]