Drush vs Composer with Drupal 8


I’ve another site with Drupal 8.3.7 that has not been installed with Composer 🙁

How can I update it to Drupal 8.5.3 ?

Should I migrate it into a Composer installation or is it still upgradable with drush8  ?

Thank you very much


Drupal version: 

Source: https://www.drupal.org/taxonomy/term/21/feed