Shipping Magnate

This really means "create 5 outpost connection links".

To link two outposts you need to build a Cargo Link at each one, and use the UI in one of them to tell it to link to the other side.

There are two levels of Cargo Link, the first is for connections in the same system only and doesn't require any special research. Or, you can upgrade your skills for Inter-System Cargo Links to ship cargo from one system to another. Only the basic Cargo Links are required for this achievement.