Hello there, New.
It sounds like you are being prompted to use mobile data when playing music from your iPhone 5s. It sounds like you may need to make that content playable offline first. The following Knowledge Base article offers up how to do that:
Add music from the Apple Music catalog to your library on your iPhone, iPad, iPod touch, Mac, or PC - Apple Support
https://support.apple.com/en-us/HT204839
You can download songs, albums, or playlists to your device so that you can listen to them when you're not connected to the Internet.* You must download songs, albums, or playlists on each device that you want to use for offline listening.
*You can download music on up to 10 devices. These songs are accessible only during your Apple Music membership.
- In the Music app, find the item that you want to download.
- Tap the More Options icon to the right of the song, album, or playlist name.
- Tap the Download icon to the right of the item's artwork. If you see a instead of the download icon, the item isn't in your iCloud Music Library. Tap the to add the item to My Music, then tap the download icon to download the item to your device.
Songs and albums appear under My Music > Library. Playlists appear under My Music > Playlists.
Thanks for reaching out to Apple Support Communities.
Kind Regards.