They could develop a mentor - mentee relationship. Itachi, with his vast knowledge and skills, could guide Naruto. Naruto, in turn, could show Itachi his unwavering spirit, which might even inspire Itachi in some ways.
In this fanfiction, Naruto might be shown as an even more precocious and determined character. Since he graduates at 5, he could have shown extraordinary skills and intelligence from a very young age. Maybe he has already mastered some basic jutsus better than his peers, which could lead to some jealousy among them.
One possibility is that Naruto has a secret training regime that he has been following. This extra training gives him an edge over his classmates. He could then participate in a tournament within the academy where he completely outperforms everyone. His display of strength, speed, and strategic thinking would be so impressive that the academy decides to graduate him early.
It could be Orochimaru. Since Naruto is graduating early and showing great potential, Orochimaru might see him as an interesting target for his experiments or as a threat to his future plans earlier than in the original story.
One interesting aspect of Naruto Rule 63 Itachi fanfiction could be exploring Itachi's character from a different gender perspective. In these fanfictions, Itachi might have different relationships with other characters. For example, his bond with Sasuke could be portrayed in a new light, perhaps with more emotional nuances due to the gender - swap. Also, the way he approaches his mission and his loyalty to the village could be re - examined through this new lens.
Well, in such a fanfiction, Naruto might face new challenges earlier. He could be thrown into more dangerous missions right away. Maybe he'd have to quickly prove himself to his peers and superiors who are skeptical of his early graduation.
It could be Orochimaru. Even though Naruto graduates early, Orochimaru might see him as a threat and try to eliminate him. Orochimaru is always on the lookout for powerful ninja to either recruit or destroy.
Their relationship could be developed through a series of flashbacks. For instance, Itachi could recall moments from Naruto's childhood that he observed while in the ANBU. These memories could make him see Naruto in a new light. Meanwhile, Naruto could learn about Itachi's past and the sacrifices he made. This exchange of knowledge could build a bond between them based on empathy and respect. In addition, they could train together in secret, with Itachi teaching Naruto some of his ANBU skills, which would also strengthen their relationship.
Naruto would adapt to Itachi's life in several ways. Socially, he'd have to get used to Itachi's connections and rivalries. For instance, his relationship with Kisame would be different as Naruto. He might try to influence Kisame in a more positive way. Emotionally, he'd have to deal with Itachi's internal struggles. Itachi had a lot of guilt and secrets, and Naruto would have to either come to terms with them or find a way to resolve them. And in terms of combat, he'd practice Itachi's signature moves over and over to make sure he could use them effectively in battle.
They could develop a mentor - mentee relationship. Itachi uses his knowledge of the Sharingan to teach Naruto new combat techniques. As they train together, they bond over their shared experiences of loss and their desire to protect the people they care about. Naruto might also help Itachi come to terms with his past actions and find some peace within himself.