You've got some PHP application that isn't 100% compatible with PHP 5.4+, and you're restoring the account to a server that is running PHP 5.4+.
If your host allows you to modify your PHP ini and modify error_reporting to be something like this:
error_reporting = E_ALL & ~E_NOTICE & ~E_STRICT
If your web host uses PHP selector to allow to choose the version of PHP version via the cPanel interface, either select a version of PHP that is compatible with your current PHP application or modify the PHP settings, specifically the error reporting.
Mike
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Or, if you are the admin of the cPanel server:
Do one or more of the following:
1. WHM --> EasyApache -- build a new Apache/PHP version that is compatible with your scripts, such as PHP 5.3.27
and/or
2. Edit /usr/local/lib/php.ini
find the "error_reporting" line and set it to something like this:
error_reporting = E_ALL & ~E_NOTICE & ~E_STRICT
Mike