Did he write any more books? The books I know are the 4 books, but in the last book he writes he isn't going to leave Alagaësia and is going to write more books! But here I am in 2019 and haven't heard about any more books!
A book 5 is still in writing as far as I'm aware, he did a "recent", 18/09/2018, Q/A about Book 5 on Paolini.net:
DestinyWielder: Eragon and Saphira will not be main characters in Book Five, right? They will appear as minor cameos, yes? You have said that some element of Book Five has been set up in the previous books and nobody has guessed what it is, right?
Correct. Eragon/Saphira won’t be the main characters in Book V. And yes, I laid some groundwork for Book V in the previous books. Some has been spotted. Some hasn’t. It’s fun to see reader’s enthusiasm for guessing.
In the same interview he also comments further about what is planned after Book 5:
DestinyWielder: Are you going to write more books in the world of Alagaesia after Book Five is written? If the answer is yes, how many more books are you planning on writing?
Yes. How many? I have at least three planned, but they aren’t direct continuations in the way Book V will be. Ultimately, it’s going to depend on how long I live. Lol.
The FAQ section on his website also comments on a Book 5:
Will you write another book set in Alagaësia?
I did! The Fork, the Witch, and the Worm, a collection of short stories set in Alagaësia, was released on December 31, 2018! I also still have every intention of writing Book Five, which I have already outlined. After spending so long with the world and the characters of the Inheritance cycle, I can’t bring myself to walk away from them for the rest of my life. For more info, see this article.
Is The Fork, the Witch, and the Worm the long-discussed Book Five that you said you will write?
No. The Fork, the Witch, and the Worm is the first volume of a new series of short stories set in the world of Alagaësia. Book Five will be set after the events of this volume.
He did. He's written a collection of short stories set after the Inheritance Cycle. Its called The Fork, the Witch, and the Worm.