Hi there,
I'm afraid there are no passes as good value as the Japan Rail Pass available for holders of other visas, however there are alternatives which can still save you money:
As a foreign passport holder you will be eligible for the JR-East Kanto Pass, so should you be in Tokyo this would be a good option to explore the surrounding area of Tokyo.
For other long distance discounted means of travel you could investigate highway buses, or low cost airlines such as Skymark, Peach or JetStar. While these are not as convenient as the JRPass (and you must factor in airport transfers into the low cost airline option), as you will be in Japan for 5 months you could think of visiting the sights bit by bit rather than in 1 trip?
Finally, if you don't mind not using the bullet train, you should look into the Seishun-18 kippu which does offer unlimited travel on normal JR trains (though is quite a bit slower).
Hope this helps!