Getting to Gotemba from Hakone?

The ol' parentals are coming over Japan way this summer for the first time and want to see Fuji - though not climb it. They say they'll be happy just to go up to one of the fifth stations and take in the view. Since sitting on the side of a mountain all day without climbing it sounds pretty boring, we're trying to combine it with a day trip to Hakone. We are planning to use the Odakyu Hakone Free Pass and from the various stops, it seems like there are two possible ways to get to Gotemba from Hakone.
- Take a bus to Nuzuma, then JR it to Gotemba
- Take a bus from Togendai to Gotemba

I'm losing my mind trying to find and decipher bus time tables and what not. Can anyone suggest which way would be faster? Since we are trying to fit so much in the day, I think the time concern is greater than the cost concern. Also, it seems that there should be a bus from Gotemba Station to the Gotemba 5th Station up on the mountain, but does anyone know anything about it? Costs, how often it runs, etc?

(Oh, and... Gotemba would be the most convenient of the 5th Stations to go to, right?)

Thanks, folks. I'm getting near my wits end and really just want to tell the folks that seeing Fuji from a distance will be as good as (if not better than) sitting on the side of it.

I lived in Japan many years ago and climbed mt Fuji. I cannott help with bus train schedules but you said "this summer." I do know that the mountain officially opens July and august so if they are comming before or after then than they maybe no bus servic to the 5th station. You are very correct about viewing fuji close up or from a distance. It is like the forrest and the trees. You can't really see fuji if you are standing on it if you know what I mean. There are fantastic views from lake hakone and the area. Plus Gotemba is some distance from the 5th station. My recommendation would be to find an inn or restaurant with a view of the lake and mountain in the distance and have lunch and take a walk with the mountain at a distance. They will have to trust you that this is better than anything that you could see at the 5th station. If they insist on having "been on the mountain" than your stuck.. good luck.