You can use an ArrayList to store the letters (and the empty cells, I'm using a dot . so you can recognize it in the output), then use Collections.shuffle() to put elements of the ArrayList in "random" places. Finally assign each letter to the String[][] array:
public static void main(String[] args)
{
String[][] board = new String[5][5];
List<String> letters = new ArrayList<>();
// fill with letters
for (int i = 0; i < 3; i++) {
letters.add("A");
letters.add("B");
letters.add("C");
letters.add("D");
letters.add("E");
}
// fill with "empty"
for (int i = 0; i < 10; i++) {
letters.add(".");
}
Collections.shuffle(letters);
for (int i = 0; i < board.length; i++) {
for (int j = 0; j < board.length; j++) {
board[i][j] = letters.get(i*board.length + j);
}
}
for (int i = 0; i < board.length; i++) {
for (int j = 0; j < board.length; j++) {
System.out.print(board[i][j] + " ");
}
System.out.println();
}
}
Output Sample:
C B . . .
A E . E A
. A . D D
C . . . D
B C E . B
Note:
The operation i*board.length + j will generate consequent numbers 0, 1, 2, 3, ... 24 en the nested loop.