仅针对特定值执行SET？

$x = 5;
$stmt = $db->prepare('UPDATE ' . $table. ' SET sort = sort + 1') ;
$stmt->execute();

How can I execute the query only for those values in sort column which are equal or higher than $x ?

Simply add it to as where statement:

$stmt = $db->prepare('UPDATE ' . $table. ' SET sort = sort + 1 where sort >= ?') ;
$stmt->bind(1, $x)