Were you on 7.0.4 previously or on an older update? 7.0.05 only introduced changes to the broken link checker, so it does not change anything that could introduce 500 errors.
Have you tried enabling error logging on your site via the wp-config.php file, then checking the resulting log (located in /wp-content/debug.log) to see what the problem might be?
The lines to have in your config file are:
define( 'WP_DEBUG', true );
define( 'WP_DEBUG_DISPLAY', false );
define( 'WP_DEBUG_LOG', true );
If you had not updated in a while, then we’ll have to look deeper into what is causing this issue on your site.