It doesn't happen very often, but sometimes your server reports a "Error 500" after the input of a wrong user name or a wrong password in Joomla 2.5 Login, if you previously changed some settings. This tutorial shows you, what could be the trigger.
Cause of this error is either a linking error or/and wrong directory- or file permissions.This two steps could be solve this problem.
Step 1:
Check, if you set the directory- and file permissons of your tmp-directory and log-directory correctly. You find both directories in the main directory of your Joomla CMS. Both directories will be displayed in the System Informations of Joomla 2.5 Backend by using this path: "Joomla 2.5 Backend - Site - System Informations - Directory Permissions".
Step 2:
Check, if you set the path of your tmp-directory and log-directory correctly in the configuration.php of your Joomla CMS. You can find the configuration.php in the main directory of your Joomla CMS. Edit this file and check the paths in line 56 and 57.
Both path should be in the same way:
public $log_path = '/www/htdocs/your username/your Joomla main directory/logs';
public $tmp_path = '/www/htdocs/your username/your Joomla main directory/tmp';
Maybe it helps you further!