8.5.6 Update not being recognized
Unless you created your site using composer create-project drupal-composer/drupal-project, Drupal core is not actually a dependency of your project; instead your composer.json file likely contains the line "name": "drupal/drupal". Effectively, your root composer file is the Drupal core package.

In this case you can only upgrade by manually downloading the new release.

See also: Why does &quot;composer update drupal/drupal&quot; not work?

Edit:

If you want to convert an existing D8 site to the composer-based workflow, the following steps should get you most of the way.


In a different location, use composer create-project drupal-composer/drupal-project:8.x-dev &lt;my-new-site&gt; to create the new project. (Confirm the removal of the existing git history, and if you are using version control, use git init; git add .; git commit to initialize the new repository.)
Look at the contrib modules installed in your current site's modules/ folder, go into the new project, and use composer require drupal/module1 drupal/module2 [...] to install them. (Any custom modules should be copied into the folder ./web/modules/custom/ in the new project.)
Copy the contents of your sites/ folder into the ./web/sites/ folder of the new project.
After backing up your database, go into your new project folder, and use vendor/bin/drush updatedb or vendor/bin/drupal upex to update your database with Drush or Drupal Console (both are installed by default).


At this point, your new project should be ready to serve the site; change your webserver configuration or symlinks to point at &lt;my-new-site&gt;/web (the web subdirectory, not the project folder itself).