SMTP Blocked from VPS PHP Script

Hi,
I've got a PHP script which uses the Swift Mailer library to send email via SMTP from PHP.

The script works just fine when I run it from my local machine (using my VPS as the SMTP server), but when I deploy the script to my VPS, it gives a connection timeout error when it tries to connect to my mail server.

Any ideas as to what the problem might be on the VPS?