Hi please check whether the JR pass is the
day 1 July 5
Travel tokyo to Tsuragushimo
Day 3 Tokyo
day 4 shizioka
Day 6 Nagoya
Day 8 Kyoto
Day 10 Matsumoto
Day 13 Matsumoto to Tokyo
I would be staying a few days in these cities leaving Japan July 19 from Tokyo
Which train pass would be cheapest
For such a trip you'll be looking at a 14 day rail pass which costs ¥45,100. To know if it will make most sense to you, lets take a look at the equivalent costs if you were to buy the tickets outright:
TOTAL: ¥37330 for 5 legs
As you can see, individual tickets may be ¥7770 more economical in your case. However, if you included travel to and from the airport (~¥5000), and take into account that all further JR travel will be free, including all the JR lines in Tokyo (here's map of JR lines in Tokyo for reference) and day trips to Nara, Osaka, Himeji and Hiroshima from Kyoto, then you may find that a 14 day Rail Pass is worthwhile.
Please note that for Tsurugashima you'll need to use non-JR lines (for a small fee). Here is a sample itinerary for you of this trip.
Hope this helps!