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$('.js-mySelect2').select2({
  dropdownCssClass: "custom-dropdown"
}).on("select2:open", function (e) {
  var self = $(this);
  self.on('keyup', function(){
    console.log(self.val());
    console.log('fru');
  })
});

$(document).on('keydown', '.custom-dropdown .select2-search__field', function (ev) {
  var self = $(this);
  if( self.val().length > 5) {
    console.log(self.val());
  }
});

<label for="mySelect2">
    Select one...
    <select class="select2 js-mySelect2" id="mySelect2">
      <option value="">Lorem</option>
      <option value="">Ipsum</option>
      <option value="">Dolor</option>
      <option value="">Sit</option>
      <option value="">Amet</option>
    </select>
  </label>