I have an office 365 account and can't get it to send emails. But my regular shared hosting mail sends it just fine.
I use Magepal SMTP. I tried others on their demo stores but it does same thing, throw an error:
5.7.3 Authentication unsuccessful [GVAP278CA0009.CHEP278.PROD.OUTLOOK.COM]
You can use Mageplaza, this is very good plugin:
https://www.mageplaza.com/magento-2-smtp/
Or Mandrill
https://github.com/ebizmarts/magento2-mandrill
If you are able to send email from any other mail system (gmail, Yahoo Mail, Mail.com etc), then this issue is not related to any Magento extension, it's a mail server side issue.
Here are some suggestions :
There are solutions given on Microsoft community, please check once here :