Converting old website into localhost website

You should be able to find the error in the error log.
But that is not the optimum way to update a site. Each release could have changes to the database, and this function is called whenever the update is done through the Update panel in the admin. If you just copy the files, the steps could be out of order, causing an error such as you saw.

Thank you for the tip. I have to test and see. ??

With WP 5.0.2 the next errors on the site with Twenty Ten theme. :O

Fatal error: Uncaught Error: Class 'WP_Block_Type_Registry' not found in /home/umate/xxxxxxxxxxxx/wp-includes/script-loader.php:2421 Stack trace: #0 /home/umate/xxxxxxxxxxxx/wp-includes/class-wp-hook.php(286): wp_enqueue_registered_block_scripts_and_styles('') #1 /home/umate/xxxxxxxxxxxx/wp-includes/class-wp-hook.php(310): WP_Hook->apply_filters('', Array) #2 /home/umate/xxxxxxxxxxxx/wp-includes/plugin.php(453): WP_Hook->do_action(Array) #3 /home/umate/xxxxxxxxxxxx/wp-includes/script-loader.php(2405): do_action('enqueue_block_a...') #4 /home/umate/xxxxxxxxxxxx/wp-includes/class-wp-hook.php(286): wp_common_block_scripts_and_styles('') #5 /home/umate/xxxxxxxxxxxx/wp-includes/class-wp-hook.php(310): WP_Hook->apply_filters('', Array) #6 /home/umate/xxxxxxxxxxxx/wp-includes/plugin.php(453): WP_Hook->do_action(Array) #7 /home/umate/xxxxxxxxxxxx/wp-includes/script-loader.php(2231): do_action('wp_enqueue_scri...') #8 /home/umate/xxxxxxxxxxxx/wp-includes/class-wp-hook.php(286): wp_enqueue_scripts('') #9 /home/umate/xxxxxxxxxxxx/wp-includes/c in /home/umate/xxxxxxxxxxxx/wp-includes/script-loader.php on line 2421

That message looks like there is a plugin that is trying to load something for a block, but the block stuff isn’t there. Are you sure that is WP 5.0.2? Do you have an old or new Twenty Ten theme?

WP is 5.0.2 and Twenty Ten is the newest one.

I tested different versions of WP – version 4.9.9 is the last version, which is working correctly in localhost installation (Apache 2, Ubuntu Mate 18.04).