JR East Pass an option?

Hi there
We are travelling to Japan at the end of the month for 10 or so days. We fly into Narita then have three nights in Tokyo before catching the train from Shinjuku to Hakuba (direct) on 1 January. We intend to catch the bullet train from NAGANO to Shinjuku on 7 January then head down to Hakone for one night. I was thinking of buying a Hakone free pass for this but would probably return to Tokyo the next day via Shinkansen. We will need to get back to Narita in order to fly out on the 9th.
Is the JR East Pass (5 days out of 14) a good option for us? Will it cover all of our planned routes except for the trip to Hakone?
I would appreciate your advice.
Many thanks