His relationship with his parents would be very strange. If he goes back to a time when his parents were alive, he would have to hide his true identity. But he could also get to know them in a way he never did. He might be able to change their fates as well, which would have a huge impact on his own life and the entire Hidden Leaf Village.
Naruto's relationship with the other villagers would also change. In the past, many villagers were afraid or hostile towards him because of the Nine - Tails inside him. But as a 7th Hokage traveling back, he has proven himself. He could use this to change how the villagers see him in the past and maybe even make the village a more inclusive place from an earlier time.
His relationship with his teachers would also change. For example, with Iruka - sensei, Naruto could show his gratitude in a more profound way. He could also use his skills as the Seventh Hokage to help Iruka in ways he couldn't before. And with Kakashi - sensei, Naruto could offer insights into future threats and how to better train the next generation, strengthening their bond as teacher and student even more.
If Naruto travels back to the past, his relationship with his parents would be completely different. He would finally get to meet them as an adult and be able to have proper conversations with them. He could share his experiences and they could give him advice from their own wisdom.
His relationship with Sasuke would likely become more of a partnership. As Hokage, Naruto would need Sasuke's skills and knowledge to protect the village. They would probably have regular meetings to discuss security and other important matters.
Her relationship with Sasuke would be very different. If she time - travels back, she might be able to approach Sasuke in a more mature way as a Hokage. Instead of just chasing after him out of friendship and rivalry, she could offer him real solutions to his problems and help him find his place in the village without leaving.
Under Naruto as the 5th Hokage in fanfiction, the village would experience a cultural shift. Since Naruto values all kinds of people, the village would be more open to different ideas and ways of life. New forms of ninja techniques might be developed as he encourages everyone to explore their potential. Also, the village's defenses would be strengthened not just by physical means but also by the strong bonds between the villagers, which Naruto would foster.
Another idea for this fanfiction is that Naruto's time travel as the 6th Hokage could lead to him meeting his predecessors in a different way. He could learn new jutsu or leadership skills directly from them. For instance, he could have in - depth conversations with the 1st Hokage, Hashirama, about how to better manage the relationships between different ninja clans and build a stronger, more united village.
His relationship with his former sensei, Iruka, would be really interesting. Naruto could go back and show Iruka how much he has achieved, which would be a really heartwarming moment. And with Kakashi, he could share his experiences as Hokage and maybe even learn some new things from Kakashi in the past.
Well, Naruto could go back in time and train his younger self. He'd be able to pass on all the skills and knowledge he has as the 6th Hokage. This would make his younger self much stronger and more confident much earlier in life.
It could strengthen Naruto's relationship with Iruka. Since Naruto is the son of the fourth hokage, Iruka might see Naruto as an even more important part of the village and be even more protective. For example, he could be more involved in Naruto's advanced training.
In fanfiction, Naruto's rule as the 5th Hokage might be full of positive changes. He would probably focus on improving relationships between the different ninja clans in the village. He'd also likely invest a lot in training the new generation of ninjas, using his own experiences to teach them about perseverance and the importance of friendship.