Infinity178,
<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>sortable demo</title>
<link rel="stylesheet" href="https://code.jquery.com/ui/1.12.0/themes/smoothness/jquery-ui.css">
<script src="https://code.jquery.com/jquery-1.12.4.js"></script>
<script src="https://code.jquery.com/ui/1.12.0/jquery-ui.js"></script>
</head>
<body>
<ul id="sortable">
<li>Item 1</li>
<li>Item 2</li>
<li>Item 3</li>
<li>Item 4</li>
<li>Item 5</li>
</ul>
<input name="" type="button" value="Ajax" class="btn">
<script>
$("#sortable").sortable();
$(".btn").on('click', function() {
$("<li>", {text: "Item "+ ($("#sortable li").length+1)}).appendTo("#sortable")
$( "#sortable" ).sortable( "refresh" );
}
)
</script>
</body>
</html>