Laravel 5 Delete existing Article with destroy method

The reason is because you are using a tag. Use the form tag with method equals to delete which will solve your problem.

          @foreach($articles as $key => $article)
            <tr>
             <td class="td-actions text-right">
                <a  href="{{action('ArticlesController@edit',$article->id)}}"type="button" rel="tooltip" title="" class="btn btn-info btn-simple btn-xs" data-original-title="Edit Article">
                  <i class="fa fa-edit"></i>
                </a>

                {{ Form::open([ 'method'  => 'delete', 'route' => [ 'items.destroy', $item->id ] ]) }}
                    {{ Form::submit('Delete', ['class' => 'btn btn-danger']) }}
                {{ Form::close() }}

             </td>
            </tr>
            @endforech

Try to do like this

public function destroy($id) {
  $article = Article::findOrFail($id);
  $article->delete();

  return view('dashboard')->with([
    'flash_message' => 'Deleted',
    'flash_message_important' => false
  ]);
}

You need to use delete method to call destroy() action, for example:

{!! Form::open(['method' => 'Delete', 'route' => ['article.destroy', $id]]) !!}
<button type="submit" class="btn">Delete article</button>
{!! Form::close() !!}

You can't use a href link here.