why can't I access my music playlists on iPhone 5?

If you’re an Apple Music member, tap My Music, tap Playlists, then tap New Playlist.

If you’re not an Apple Music member, tap Playlists at the bottom of the screen.

If that's not working, please provide more details as why you're not able to use Playlists

https://support.apple.com/en-us/HT204839