How about this:
int[] myArray = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9};
System.arraycopy(myArray, 5, myArray, 4, 5);
myArray[myArray.length-1] = 4;
In the above code, I'm using the arraycopy method to copy a range of 5 numbers starting from index 5, to index 4 in the array, and then simply set a 4 in the last position.
Notice that using arraycopy is much faster than copying the values in a loop, since it's usually implemented as a native operation which copies memory positions.
EDIT :
A more generic solution, a method for sending to the back a given position in the array:
public static void sendBack(int[] array, int idx) {
int value = array[idx];
System.arraycopy(array, idx+1, array, idx, array.length-idx-1);
array[array.length-1] = value;
}
For your example, call it like this:
sendBack(myArray, 4);
// now myArray is {0, 1, 2, 3, 5, 6, 7, 8, 9, 4}