The tutorial wasn’t very clear. The buttons are in our case movie clips and then in the code we set their buttonMode property to true.
Both of you have created buttons instead of movieclip and in that case they don’t have a buttonMode property so indeed you need to delete this line of code : buttons[i].buttonMode = true;

import caurina.transitions.*;

var position:Number = 0;

var b1X : Number = 0;
var b2X : Number = -550;
var b3X : Number = -1100;
var b4X : Number = -1650;
var b5X : Number = -2200;

var locset:Array = [0,-550,-1100,-1650,-2200];

var buttons : Array = [b1_btn,b2_btn,b3_btn,b4_btn,b5_btn];

// pile funktion

back_btn.addEventListener(MouseEvent.CLICK, back);

function back(e):void {
position–;
trace(position);

var locsetlength:Number = locset.length-1;
if (position locsetlength) {
position = 0;
setTween(0);
} else {
setTween(locset[position]);
}
}

for (var i:int = 0; i< buttons.length; i++) {

buttons[i].addEventListener(MouseEvent.CLICK,navigate);
//buttons[i].buttonMode = true;
}

function navigate(event:MouseEvent):void {

switch (event.target) {
case (b1_btn) :
setTween(b1X);
position = 0;
break;

case (b2_btn) :
setTween(b2X);
position = 1;
break;

case (b3_btn) :
setTween(b3X);
position = 2;
break;

case (b4_btn) :
setTween(b4X);
position = 3;
break;

case (b5_btn) :
setTween(b5X);
position = 4;
break;
}
trace(position);
}
function setTween(tweenX:Number):void {
Tweener.addTween(content_mc, {x:tweenX, time:1, transition:"easeInOutCubic"});
}

Tweener.addTween(content_mc, {x:tweenX, time:1, transition:”easeInOutCubic”});

Thanks