Do i need a JR pass?

Hi to you team, I was so excited when a friend of mine gave me this site to explore. We are set to visit Japan in early November and while they are staying for about 10 days, I am only catching up with them for the last 5 days of the trip. Which brings me to my question, my itinerary includes the following:
day 1 - Ginkaku-ji Temple, Honen-ni Temple, Imperial Palace, Kinkaku-ji Temple, Kiyo miza temple and Pontocho in Kyoto
day 2 - Mt Fuji
day 3 - Nagoya for Toyota museum and then stay overnight at Osaka
day 4 - Kyoto sight seeing
day 5 - flight at Osaka Kinsai airport.

with this itinerary, can you kindly help me decide whether it is wise to purchase a JR pass for 7 days? will it be worth it?

Thank you so much and any help would be greatly appreciated.

:-) Sara