You are experiencing trouble because you're running a version of macOS that is not supported. Our system requirements can be found here:
And the required macOS version is also listed on our downloads page:
Postbox 5 has always specified a minimum requirement of macOS 10.10.
You can update macOS to 10.10 or higher (its free), or revert back to an earlier version of Postbox here:
http://postbox-downloads.s3.amazonaws.com/mac/postbox-5.0.18-mac64.dmg
But note that we do not support earlier versions of Postbox nor unsupported OS versions. We hope you understand.