copy files from an old c5 5.4.1.1 to a new 5.7.5.6 sql database

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Hello forum,

i would like to change our old website from c5 5.4.1.1 into a new 5.7.5.6 or maybe higher.

Hopefully this ist the right place for this post...

I will not make the updates, but i don´t wanna loose all the pictures and files and specially google-rankings of them.
So, if i would only copy the old file-folder to the new installation - the pictures could be found via the old links, but couldn´t be used via the dashboard.
My idea was, that i also need to copy some parts of the old-sql-database into the new one. I found the files in phpmyadmin, but i don´t know if need to change other folders also.
Or does there maybe exist a plugin which could transfer my old files into the new database without so much trouble??
Unfortunatelly i can´t find much in the german manual, so could please anybody give me (as a pure beginner ;-) ) some hints?!

Thank you!