Android 5.1 App Data

[darwin4ever]

I want to start using another phone but I need absolutely the App Data from some apps on my old Android 5.1 (not rooted) Phone.

I found some Backup-tools, but at most they backup the App-apk's and not the App-data, so they are of no use at all.

I really don't understand why it's so difficult to transfer App-data from one phone to another.

How can I proceed ?