Sources: Picture of the case back, plus Anison.info and Japanese Wikipedia to complete the few credits hidden under the obi:
http://anison.info/data/source/7615.html
https://ja.wikipedia.org/wiki/%E5%9C...83%9E%E3%83%B3
Also watched Wikia:
http://powerrangers.wikia.com/wiki/C...Sentai_Fiveman
SHINES is only credited for chorus for the songs ジャンケンジャンプ!ファイブマン (04) , ブラザー・ブラッド (08) and ハンド・イン・ハンド (09), if we see the CD cover back or the cassette insert front of the album "Chikyuu Sentai Fiveman Hit Song Collection" (COCC-6435):
https://vgmdb.net/db/covers.php?do=view&cover=314156
https://vgmdb.net/db/covers.php?do=view&cover=314166
For the insert/image songs, I prefer to use Wikipedia which gives the episode numbers for the insert songs.
The song Atsui Beat de Fiveman/熱いビートでファイブマン (02) is only used in instrumental version in episode 26, so I consider it like an image song.
The lyricist 曽田博久 = Hirohisa Soda
Wikipedia:
https://ja.wikipedia.org/wiki/%E6%9B...8D%9A%E4%B9%85
DrillSpin:
http://www.drillspin.com/person/view/ARDSAX048654
Weblio:
https://ejje.weblio.jp/content/%E6%9...8D%9A%E4%B9%85
The lyricist 長石多可男 = Takao Nagaishi
Wikipedia:
https://ja.wikipedia.org/wiki/%E9%95...8F%AF%E7%94%B7
DrillSpin:
http://www.drillspin.com/person/view/ARDSA0804880
Weblio:
https://ejje.weblio.jp/content/%E9%9...8F%AF%E7%94%B7
The lyricist 渡辺勝也 = Katsuya Watanabe
Wikipedia:
https://ja.wikipedia.org/wiki/%E6%B8...8B%9D%E4%B9%9F
DrillSpin:
http://www.drillspin.com/person/view/ARDSA0804780
FULTA is an alias for the composer Yoshiaki Furuta:
Wikipedia:
https://ja.wikipedia.org/wiki/%E5%8F...96%9C%E6%98%AD
DrillSpin:
http://www.drillspin.com/person/view/ARDSAX027739
The composer 広沢麻美: Asami Hirosawa?
There's a musician known as this name (with a variation: Asami Hirozawa/廣澤麻美), but I'm not sure this is the same person:
Blog:
http://saskia1217.exblog.jp/
Twitter:
https://twitter.com/musicasami
DrillSpin:
http://www.drillspin.com/person/view/ARDSAX158149