Tales of Graces f boasts 85 different discoveries waiting to be recorded in your discovery book. Here's numbers 6 through 10.
Discovery #6: Spring of Healing
On your first trek up Lhant Hill you didn't have the Discovery Book. Thankfully, you can now grab this discovery, and refresh your health as well!
Discovery #7: Abandoned Nest
On the way back up the cliffside with Richard, be sure to investigate this abandoned nest, triggering another skit.
Discovery #8: Friendship Tree
After carving your names into the trunk of the friendship tree, quickly add it to your Discovery Book. This will trigger a fun cutscene with Asbel explaining why Hubert and Cheria were left out.
Discovery #9: Windor Cows
On the way to Barona, you'll find a herd of cows standing around. Talk to the oddly branded green and orange cow multiple times, after which it will finally give up some milk, letting you add it to your Discovery Book. After a fun cutscene with Asbel fighting the cow, you'll now have a regular source of milk worth hitting up.
Discovery #10: Gloandi
West of Barona is the giant Cryas shard known as Gloandi. After meeting Richard (aka "Tiger Festival") in front of the massive monument, quickly add it to your discovery book, then enjoy a brief skit with Asbel and Sophie.