Dear Customer - Hope you are doing well. Thanks for reaching out to us via AWS re:Post.
Well, troubleshooting connectivity issues is a bit tough over this forum as it may require deep dive on the internals (security group, NACL, vpc details etc.) - Adding to the answer that has been posted already - I wanted to share this link that may help you troubleshoot.
[] Connecting to a DB instance running the MySQL database engine - https://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/USER_ConnectToInstance.html
In case they do not work, I would recommend reaching out to AWS Premium Support for a deep dive troubleshooting session. Have a great rest of the day!
Have you checked your VPC Network ACLs, and Routing?
Also if you're connecting from an office, are you sure the corporate firewall isn't blocking you?
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Thanks. I haven't this YouTube clip yet. I don't think I'm on Premium Support, but hopefully this finally does the trick. I have my work cut out for me for the weekend.