Edit in JSFiddle

#container2 > div:nth-child(1) {
  order:3;
}
#container2 > div:nth-child(2) {
  order:5;
}
#container2 > div:nth-child(3) {
  order:1;
}
#container2 > div:nth-child(4) {
  order:4;
}
#container2 > div:nth-child(5) {
  order:2;
}
.flex {
  display:flex;
  flex-direction:row;
  width:500px;
}

div {
  border:1px solid #cccccc;
  margin:5px;
  padding:5px;
}
div > div {
  background:#ffcc99;
}

原資料
<div id="container" class="flex">
   <div>Item1</div>
   <div>Item2</div>   
   <div>Item3</div>  
   <div>Item4</div>  
   <div>Item5</div>    
</div>
按照 Item3、Item5、Item1、Item4、Item2 排序
<div id="container2" class="flex">
   <div>Item1</div>
   <div>Item2</div>   
   <div>Item3</div>  
   <div>Item4</div>  
   <div>Item5</div>    
</div>