Add LabelingSize -> Full to the second PieChart:
data = {13, 17, 22, 21, 20, 0.6, 1.3, 2.4, 0.8, 1.9};
largeData = Take[data, 5];
smallData = Drop[data, 5];
smallPie =
PieChart[smallData, ImageSize -> Tiny,
LabelingFunction -> "RadialCenter",
ChartLabels -> Placed[CharacterRange["F", "Z"], "RadialOutside"]]
PieChart[Append[largeData, Total[smallData]], ImageSize -> Medium,
LabelingFunction -> "RadialCenter",
ChartLabels ->
Placed[Append[CharacterRange["A", "E"], smallPie], "RadialCallout"],
PlotRange -> All, LabelingSize -> Full]