It sounds too tight to make a one-day trip to both Hiroshima City and Miyajima Island from Osaka City; I recommend you expect at least 2 days.
When you plan to visit Nara City, Yoshino, Kobe City, Hiroshima City and Miyajima Island within 5 days, you can make a combination of
JR regular tickets to travel from Tokyo to Kyoto and back
(27200 to 27600 yen, for Shinkansen Hikari train rides)
and a JR-West Kansai-Hiroshima Area Pass
(13500 yen when booked through the official website).
http://www.westjr.co.jp/global/en/ticket/pass/kansai_hiroshima/The total amount is 40700 to 41100 yen, much less than the price 46390 yen of a 14-day (Ordinary-Class) Japan Rail Pass.
A possible merit is
that you can take Shinkansen Nozomi trains between Tokyo | Shinagawa and Kyoto on the Tokaido Shinkansen when you pay 310 yen more per way
and also take Nozomi and Mizuho trains with a JR-West Kansai-Hiroshima Area Pass between Shin-Osaka and Hiroshima on the Sanyo Shinkansen.
A possible demerit is that a JR-West rail pass is not valid on the Tokaido Shinkansen (Tokyo -- Nagoya -- Kyoto -- Shin-Osaka),
which is operated not by JR-West but by JR-Central.
To travel between Tokyo and western Japan,
alternatively you can take domestic flights at ANA | JAL discount prices
from Tokyo Haneda [HND] to Osaka Itami [ITM]
and from Hiroshima [HIJ] to Tokyo Haneda [HND].
The total amount of the discount air fares is about 18000 yen to 21000 yen,
and you may pay around 2000 yen for your airport accesses.
https://www.ana.co.jp/en/us/promotions/share/experience_jp/https://www.world.jal.co.jp/world/en/japan_explorer_pass/lp/