You have all of your types mixed up...
In my opinion, at least, it would be much easier to use ints for everything - that means casting to and int upon declaration.
For example:

1. int [] HelloArray= new int [int(random(5,11))];

here...

1. //
2. int [] HappyArray= new int [int(random(5, 11))];
3. int yBorder = 65;
4. void setup() {
5.   size(400, 400);
6.   fill(0);
7.   for (int i=0; i<HappyArray.length; i++) {
8.     HappyArray[i] = int( random(100));
9.     // int HappyArrayBest = int (random(HappyArray.length));
10.   }
11.   frameRate(1);
12. }
13. void draw() {
14.   background(255);
15.   int HappyArrayBest= int (random(HappyArray.length));
16.   fill(244, 2, 2);
17.   text("The array contains "
18.     +HappyArray.length
19.     +" items: ",
20.   50, yBorder-40);
21.   //
22.   fill(0); 
23.   for (int i=0; i<HappyArray.length; i++) {
24.     text("Item "
25.       +i
26.       +" is "
27.       + HappyArray[i]
28.       + ".",
29.     100, yBorder+i*20);
30.   } // end of for
31.   //
32.   fill(20, 215, 22);
33.   text("The random index is "
34.     +HappyArrayBest
35.     +" and contains "
36.     +(HappyArray[HappyArrayBest])
37.     +".",
38.   50, yBorder+(HappyArray.length+1)*20);
39.   println(HappyArray);
40. }
41. //

with this version you cange also the array with keystroke

1. //
2. int [] HappyArray;
3. int yBorder = 65;
4. void setup() {
5.   size(400, 400);
6.   frameRate(1);
7.   initArray();
8. }
9. void draw() {
10.   background(255);
11.   // initArray();
12.   int HappyArrayBest= int (random(HappyArray.length));
13.   fill(244, 2, 2);
14.   text("The array contains "
15.     +HappyArray.length
16.     +" items: ",
17.   50, yBorder-40);
18.   //
19.   fill(0); 
20.   for (int i=0; i<HappyArray.length; i++) {
21.     text("Item "
22.       +i
23.       +" is "
24.       + HappyArray[i]
25.       + ".",
26.     100, yBorder+i*20);
27.   } // end of for
28.   //
29.   fill(20, 215, 22);
30.   text("The random index is "
31.     +HappyArrayBest
32.     +" and contains "
33.     +(HappyArray[HappyArrayBest])
34.     +".",
35.   50, yBorder+(HappyArray.length+1)*20);
36.   println(HappyArray);
37. }
38. //
39. void keyPressed () {
40.   initArray() ;
41. }
42. void initArray() {
43.   HappyArray= new int [int(random(5, 11))];
44.   //
45.   for (int i=0; i<HappyArray.length; i++) {
46.     HappyArray[i] = int( random(100));
47.   }
48. }

here

1. int [] HappyArray= new int [int(random(5, 11))];
2. int HappyArrayBest;
3. int yBorder = 65;
4. void setup() {
5.   size(400, 400);
6.   for (int i=0; i<HappyArray.length; i++) {
7.     HappyArray[i] = int( random(100));
8.   }
9.   HappyArrayBest= int (random(HappyArray.length));
10.   // frameRate(1);
11. }
12. void draw() {
13.   background(255);
14.   // head line
15.   fill(244, 2, 2);
16.   text("The array contains "
17.     +HappyArray.length
18.     +" items: ",
19.   50, yBorder-2*20);
20.   // the list
21.   fill(0);
22.   for (int i=0; i<HappyArray.length; i++) {
23.     text("Item "
24.       +i
25.       +" is "
26.       + HappyArray[i]
27.       + ".",
28.     100, yBorder+i*20);
29.   } // end of for
30.   // the best
31.   fill(20, 215, 22);
32.   text("The random index is "
33.     +HappyArrayBest
34.     +" and contains "
35.     +(HappyArray[HappyArrayBest])
36.     +".",
37.   50, yBorder+(HappyArray.length+1)*20);
38.   // println(HappyArray);
39. }
40. //

you're welcome!

some remarks:

1.
setup and draw are functions.

void does just mean they return nothing (or emptiness/void).

you can also return a number or so (when a function adds to numbers or so).

Just say setup() or function setup(), not void setup. 


2.
draw() always loops automatically

In most cases we want that, because e.g. a ball is rolling over the screen and we want to paint it all along
therefore we start in draw() with

1.   background(255);

3.
what you mean here:

set up the background too, if not it was keeping looping...

I am not sure, cause background in setup() has not so much to do with looping...

But I am glad you achieved what you wanted!  

oh, thanks, design is definetly my weak point, thank you!  

That's great!

Please remember: With ctrl-t you can auto-format your code to get a great indent. You don't need so much empty lines in your code.

You don't have a func draw() now which is fine. But when you write code with keyPressed() or so you need draw() otherwise it won't work.

Greetings, Chrisir