{{"5", "4", "3", "2", "1"},
   {"A", 3, 1, 2, 0, 4},
   {"B", 8, 29, 55, 14, 22},
   {"C", 15, 87, 418, 728, 340},
   {"D", 41, 28, 154, 821, 939},
   {"E", 3, 21, 78, 257, 594}}

Column1    Column2    Value
A          5          3
A          4          1
A          3          2

...

E          5          3
E          4          21
E          3          78
E          2          257
E          1          594

m = { {"5", "4", "3", "2", "1"},
      {"A", 3, 1, 2, 0, 4},
      {"B", 8, 29, 55, 14, 22},
      {"C", 15, 87, 418, 728, 340},
      {"D", 41, 28, 154, 821, 939},
      {"E", 3, 21, 78, 257, 594} };

Dataset @ Flatten @ Array[
  <|"Column1" -> m[[#+1, 1]], "Column2" -> m[[1, #2]], "Value" -> m[[#+1, #2+1]]|>&
, {Length[m] - 1, Length[m[[1]]]}
]

data = {{"5", "4", "3", "2", "1"}, {"A", 3, 1, 2, 0, 4}, {"B", 8, 29,
 55, 14, 22}, {"C", 15, 87, 418, 728, 340}, {"D", 41, 28, 154, 821,
 939}, {"E", 3, 21, 78, 257, 594}};

data2 = Most[ArrayRules[SparseArray[data[[2 ;;, 2 ;;]], Automatic, Null]]];
data2 = data2 /. {r_Integer, c_Integer} :> {data[[2 ;;, 1]][[r]], data[[1]][[c]]};
Dataset[Flatten@*List @@@ data2]

columns = Join @@ Join[Outer[List,m[[2;;,1]], m[[1]]], List /@ # & /@ m[[2;;, 2;;]], 3]
Dataset[Association[{"rowLabel" -> #, "colLabel" -> #2, "value" -> #3}]& @@@ columns]

Dataset[
 Map[
  AssociationThread[data[[1]], #] &,
  AssociationThread[
   data[[2 ;;, 1]],
   data[[2 ;;, 2 ;;]]
   ]
  ]
 ]