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Based on the comments and additional info.
The inbound rule for 5432 port is set to security group sg-597. This allows for inbound traffic only from other instances that have the same sg, not from the internet.
To enable access to the rds from the internet have to use either 0.0.0.0/0 as the source (i.e. all source locations), or which is better, specific IP range or address (e.g. 1.2.3.4/32). The range can be the range of your work or home public network, and IP can be the specific address of your workstation.
Source:stackexchange.com