How to update from Drupal core 8.5.0 to 8.5.5?
It's all here Update core via Composer.

Short version, turn on maintenance mode

drush sset system.maintenance_mode 1


then run

composer update drupal/core --with-dependencies
drush updatedb
drush cr


Turn off maintenance mode

drush sset system.maintenance_mode 0



  If you run the composer update command above but drupal/core is not
  updated, there might be another dependency holding back the Drupal
  upgrade. You can check for blocking dependencies using the command
  composer prohibits. For example, if you are trying to upgrade from
  8.4.5 to 8.5.0, you can run composer prohibits drupal/core:8.5.0, and it should give a list of dependencies blocking the upgrade. Update
  those dependencies along with drupal/core and it should work (e.g.
  composer update drupal/core symfony/* --with-dependencies).