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DigitalOcean denies emails being sent on port 25 as they are most often than not spam. With that being said that’s why you’ll need to use postfix and port 465 for sending out e-mails.
On to the problem itself, the most common issues that occur with the error message you’ve provided are :
Reconfigure Postfix
sudo dpkg-reconfigure postfix
Hostname Differs
hostname in /etc/hostname and the name for 127.0.0.1 in /etc/hosts differed.
If the above doesn’t help, I’ll recommend checking out the mail error log in your /var/log folder for further information on the exact issues that are stoping the e-mails from being sent.
Regards, KFSys