Advance tickets to Fuji Five lakes region

Should we book bus tickets in advance for a trip from Shinjuku Station to Fuji Five lakes region? They run a lot of busses, so it looks unnecessary, but we wouldn't want to miss out.

Depending on the day, they can get booked out.
I recommend to make advance reservations.
If you want to remain flexible, you could always take the train instead in case the buses are booked out.