What's the best way to get back to Shinjuku from Mt. Fuji's 5th Station?

by Alex
(Long Beach, CA, USA)

First off - love the site. I've been on this site for the past 5 hours and the information here is phenomenal.

Scenario: a friend and I were planning to take the bus from Shinjuku to 5th station. Leave around 6-8 to arrive around 9-10 am. We plan on doing the hike and if it takes 8-10 hours, this would leave us back at the 5th station around 6-8 pm (we're taking the Yoshida trail as our planned trek is on July 7th, which is before the other 3 trails are open, thanks to your info).

Question: what's the best way to get back to Shinjuku (or anywhere in Tokyo) after our hike is completed. we definitely need to be back in Tokyo as we cannot stay the night in Fuji (due to time constraints). I notice the last bus heading back to Tokyo from 5th station is at 15:00 (or 3 pm). Are there taxis that are around 5th station throughout the entire night?

Thank you so much for all that is on here.