A couple of things you can look at here.
You are using "SEPM 11.0.x" correct?
From what I can see, you are trying to use port 587 (TLS) for SMTP settings.
"As more email providers move to requiring encrypted connections to their servers a need has arisen for complete support of the major protocols in use. The Symantec Endpoint Protection Manager presently supports SSL connections but lacks the support for TLS encryption. Since TLS has grown in popularity some major email providers have begun restricting email traffic to TLS only. This removes the possibility of a plain-text or SSL connection and reduces the number of servers that will accept mail from the Symantec Endpoint Protection Manager. Please consider adding TLS support in order to meet this need and provide for the best Notification and Reporting system, since TLS is not going away and may soon replace SSL email in many environments."
Please add a vote for this:
https://www-secure.symantec.com/connect/ideas/add-support-tls-email-encryption-symantec-endpoint-protection-manager
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The solution to your problem is use port 465 (SSL) instead of port 587 (TLS).
This may STILL NOT WORK, because it is possible, GMAIL wants to explicitly indicate to use SSL (which is not supported in your version of SEPM) - see screen shot.
So, if you cannot use port 465 to send an e.mail from "smtp.gmail.com" you may want to try have the mail sent via port 25.
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Cheers!!