From the Super Mario Wiki
The Journal Entries are items that appear in Paper Mario: Color Splash. They were written by the Legendary Captain, and they explain how to get through the Lost Sea. The Toad Captain tells Mario that the pages were missing when the Legendary Captain's journal was found on the ship. There are five in total, and they can be found on the Toad Captain's ship. Mario must find them for the Toad Captain and give them to him. Once Mario gives all of the entries to the Captain, the ship can set sail for Fortune Island. The Journal Entries will always be collected in order.
Locations of the Journal Entries
Journal Entry Messages