Errors upgrading from 8.3.7 to 8.5.3


For the past couple of weeks, I’ve been trying to upgrade to the latest Drupal. I’ve tried different ways but still got no further. Here are my current settings:

Current Version:
Drupal 8.3.7
php 5.6
Drush 8
Composer 1.4.1

Drupal 8.5.3
php 7.2
Drush 9
Latest Composer

How I usually upgrade:
Manually take backup of /core and save it. Replace old core with new core directory. Then run update.php from site. Unfortunately, it doesn’t work for this process.

Issues started showing once I try to run “../vendor/drush/drush/drush cr” from /web directory

Examples of errors outputted:

PHP Fatal error:  Declaration of DrupalComponentDependencyInjectionContainer::set($id, $service) must be compatible with SymfonyComponentDependencyInjectionContainerInterface::set($id, $service, $scope = self::SCOPE_CONTAINER) in /var/www/html/web/core/lib/Drupal/Component/DependencyInjection/Container.php on line 47

PHP Fatal error:  Uncaught Error: Class ‘DrupalCoreDrupalKernel’ not found in /var/www/html/web/index.php:16nStack trace:n#0 {main}n  thrown in /var/www/html/web/index.php on line 16

PHP Warning:  require(/var/www/html/vendor/composer/../symfony/polyfill-php70/bootstrap.php): failed to open stream: No such file or directory in /var/www/html/vendor/composer/autoload_real.php on line 66
 PHP Warning:  include(): Failed opening ‘/var/www/html/vendor/composer/../../core/lib/Drupal/Core/DrupalKernel.php’ for inclusion (include_path=’.:/usr/share/pear:/usr/share/php’) in /var/www/html/vendor/composer/ClassLoader.php on line 444


I’ve tried using composer to upgrade but I haven’t used it before and had no success so far. 

How my folders are setup:

Under /html directory: vendor/ , composer.json, composer.lock, web/

Under web/: core/ , themes/, modules/, composer.json, etc. 

Any help would be appreicated. 

Drupal version: