/path/to/php
and /path/to/api/cron.php
These need to be the actual paths to PHP and your cron.php file for your particular installation. These need to be the absolute paths on the server (relative paths don't always work), and has nothing at all to do with your domain name.
If you need to know where PHP is located, contact your system admin.
Alternately, you could try
*/5 * * * * php -q /path/to/api/cron.php
The path will be something like /home/vculp/www/osticket/api/cron.php
You can create a new PHP file with the following code and upload it to your api directory, then point your browser to it and get the full path, if you're not sure what it is.
<?=$_SERVER?>
I'd recommend deleting the file after you get the info you need.