transport in Japan

Your decision is correct, when you happen to feel like making a day trip from Osaka/Kyoto to Hiroshima/Miyajima, consider to buy 7 day JR Pass.

A full JR Pass would not pay off. Some regional passes can save you a lot of money though.
Have a look at:

http://www.japan-guide.com/e/e2357.html

It's unclear why you want to spend 5 days in Toyama. There are some sights to see of course, but nearby Takayama, Kanazawa, plus Shirakawa-go & Gokayama are excellent places to visit.
For the Kansai area, Himeji Castle is also excellent.
You could also use the Wide Pass to go to Okayama. It has Korakuen, one of Japan's top 3 gardens, and the Handayama Garden there has beautiful cherry blossoms with the huge tourist crowds.

https://www.youtube.com/watch?v=5zAI3_N7NEM

https://www.youtube.com/watch?v=JGQ8o7k9GbA

Thank you very much for your advice and sightseeing suggestions.
The reason I'm going to Toyama is to see part of the Tateyama Kurobe Alpine route, if the weather permits.
I will also be visiting the surrounding areas of Takayama.

By the way, is there a new Shinkansen service I can take from Tokyo to Toyama?

sure http://www.japan-rail-pass.com/japan-by-rail/travel-tips/hokuriku-shinkansen