The Shipping Magnate achievement description is not written to accurately reflect how to unlock the achievement. It requires a total of 6 outposts, not 5 outposts to pull off. Before starting on the achievement make a manual save, go to a resource/materials vendor, like Jemison Mercantile shop in the New Atlantis star port. From there, purchase the following materials. If the vendor runs out. Sleep for 48 hours and return to buy more until you hit the needed quantities.
72x Aluminum
12x Beryllium
120x Iron
12x Zero Wire
Once you have all required materials, open the planetary map and land in an area outside civilization. This can easily be done on Jemison where New Atlantis is located. Exit your ship, press LB to bring up the Scanner, press X to enter the outpost build menu, and place an Outpost Beacon. Then, press LB/RB to scroll over to the Misc. build category and build a single Cargo Link. These are massive structures that take up a large piece of real-estate.
With the Cargo Link down, run outside the buildable area of the outpost until you are able to place another Outpost Beacon. Do so, followed by another Cargo Link. This time, use the stairs on the outside of the Cargo Link to reach the roof and interact with the terminal. Select the Cargo Link node under Outpost 1 and press A to connect the two outposts. If done correctly, you should see a green icon indicating the outposts are connected.
Repeat the process building a total of 6 outposts with Cargo Links. The 4th outpost should link to the 3rd, and the 6th outpost should link to the 5th. After links have been established (3 in total), the Shipping Magnate achievement will unlock. Feel free to reload your save file and sell off the resources.