[j0hnik]

VSEM-DOBRA,
все проще простого

var arr = ['A','B','C','D','E'], a =[], x=[];

for(var k = 0; k<arr.length; k++){
	a[0] = arr[k];
	for(var l = 0; l<arr.length; l++){
		a[1] = arr[l];
		for(var m = 0; m<arr.length; m++){
			a[2] = arr[m];
			for(var n = 0; n<arr.length; n++){
				a[3] = arr[n];
				x.push(a.join(''));
			}
		}
	}
}
console.log(x);