A likely cause for the 500 Internal Server Error when activating or using a plugin is that the PHP memory limit is exhausted.
The solution to this is to raise the PHP memory limit and there are several options to do that, try these in order but make a backup of your WordPress site and its database first.
Edit your site’s wp-config.php (you will find this file in your site’s root folder) and add this line:
define('WP_MEMORY_LIMIT', '128M');
If you still see issues, depending on the amount of memory required but all plugins installed, you can also raise the value to 256M etc.
You can also try to raise the limit by editing your php.ini file:
memory_limit = 128M;
Another option is to add this line to your .htaccess file:
php_value memory_limit 128M
If you still see issues, then you should ask your hosting provider to raise the limits.