Composer won't update Drupal Core, can't determine what is stopping it
I found some other threads that highlighted webflo/drupal-core-require-dev as being an issue,
In CLI I ran

composer show


This showed me that webflo/drupal-core-require-dev was set to 8.6.3

So I ran update in CLI:

composer update drupal/core webflo/drupal-core-require-dev --with-dependencies


This updated the require version to 8.6.5.
Upon checking Drupal Status Report it also triggered a warning requiring Database updates, so I ran:

drush updatedb


and approved"yes" to the 2 updates.

This removed the Database error from Status Report and I then ran the core update CLI again:

composer update drupal/core --with-dependencies


This time it worked, so I cleared cache and turned off maintenance mode:

drush cr
drush sset system.maintenance_mode 0


and the Status Report is now clear of errors and warnings.