Why doesn't core get updated to 8.5?
A few things to try if composer update drupal/core --with-dependencies doesn't work

If you're composer.json contains these lines, remove them (where XX equals anything)

"replace": {
    "drupal/core": "~8.XX"
},


Then run composer require drupal/core:~8.5.1 (even if your composer.json did not contain the above lines)

If that fails, try my last ditch method:

Remove the core &amp; vendor folder (we will then re-add)

sudo rm -rf core vendor


Clear Composer cache

composer clearcache


Then again

composer require drupal/core:~8.5.1


Don't forget to make a backup first if you haven't already!