For a start I'd suggest you use mouseReleased() instead of pressed, since the latter repeats for as long as the mouse is held - i.e. it will pretty much always get called several times on any given 'single' press.  Next, you need to check that the value of count doesn't reach or exceed the length of the array or you'll get the NPE.  That's just a matter of wrapping count++ in a condition: if it's equal or greater than the array length set it back to zero ;)

As I wrote very recently, you made a very common error. Not sure why this error comes up so often... I suppose we should have a warning when a local variable shadows a global one (Alex in your case). Actually, IDEs like Eclipse do the warning, at least.
In short, don't re-declare Alex in setup(): don't put the type in the line initializing it.

@blindfish

for what philho said.
by writing :

1.   PImage[] Alex = new PImage[5];

you declared a new Array.
instead just write

1.   Alex = new PImage[5];

in setup.

oh and depending on your larger code, it might be useful to use a loop to load the images.

for ( int i = 1; i<= Alex.length; i++ ){
Alex[i] = loadImage( "Alex"+ i + ".jpg" );    
}
 

So is this the proper way ?

yes.

for the loop, still saved 3 lines ;)

You can initialize the array's dimension either in the declaration (outside of setup()) or inside setup(), both are correct. There is not always a "proper way" (in the sense of unique), but there are several improper ways, alas...
The initialization of the content of the array is better done (here, it is even mandatory) in setup(), though, as it is only then that the path to the data folder is known.