I have some audio recordings on an Android device that I wish to transfer to my iPhone 5s. I don't get a solution using iTunes.
I have to say that there are a ton of files and i don't want to have copies in the iTunes.
There are various ways this can be accomplished. A simple solution would be use a online file sharing service such as Dropbox, Google Drive, Box etc. Simply install the chosen app on your Android device and backup files using chosen service.
This should be straightforward as Android allows file system access in general and there are various 3rd party apps which will allow you to browse the device filesystem.
Once the files are synced (uploaded to the cloud services's server), simply install the iOS counterpart of the same app and access the files. You will not automatically get access to the audio files in your iOS device. However, depending on the container format of the audio files, you may be able to playback them in the cloud service app itself (Dropbox, Google Drive, Box etc.).
However, the most likely case is that you indeed wish to playback the audio files on your iOS device. In that case, it would be advisable to install VLC for Mobile app for iOS and copy over the files using file sharing feature build into iTunes for desktop.
For the aforementioned, you'll need access to a desktop computer. Simply connect your Android device to the computer and copy over the audio files to your computer. Now install iTunes desktop app and connect your iOS device. Make sure you have already installed VLC for Mobile app for iOS. Now select your device within iTunes, select file sharing in the sidebar, click on VLC and drag & drop to copy over the audio files.
This will effectively copy the files into your iOS device. However, the files will be accessible only within VLC for Mobile app. However, it's highly likely that you'll be able to playback them as VLC for Mobile app supports a vast variety of formats.