(* We define a function, diceSampleSpace[n], that lists all possible outcomes whan n dice are rolled.  This is a recursive definition. *)

diceSampleSpace[1]=Table[{i}, {i,1,6}];
diceSampleSpace[n_]:= diceSampleSpace[n]= Flatten[Map[Table[Append[#,i], {i,1,6}]&, diceSampleSpace[n-1]], 1]

(* Here is the sample space when 2 dice are rolled.*)

diceSampleSpace[2]

(* Here is the sample space when 5 dice are rolled.*)

myss=diceSampleSpace[5]

(* We sum each outcome. *)

lengthmyss=Length[myss]

sumsmyss=Map[Plus@@#&, myss]

(* We tally and then sort the summed outcomes. If {x, n} is in the list below, it means that the sum x appears n times in mysumss. *)

tallies = Sort@Tally[sumsmyss]

proportions = Map[{#[[1]], N[#[[2]]/lengthmyss]}&, tallies]

ListPlot[proportions]