Why won't my iphone 5 play all of my itunes songs without wifi access?

Go to iTunes>Preferences>Sharing

check the box against "Share my library on my local network"

Select Radio button for either "Share entire library" or "Share selected playlists"

Then click OK

Sync your device

Once your music is in iCloud, you can play it from any of your devices. Just browse the complete list of all your music stored in the cloud and tap to play to it. You can store up to 25,000 songs in iCloud (more if songs are purchased from the iTunes Store), but only what you play or download is stored on your device. Tap the iCloud download button to download music from an artist, album, or playlist. So you have immediate access to a huge music library without having to worry about the storage space on your device.

Could this be the issue? Perhaps you haven't played or downloaded in iCloud in order to have it stored on your device.

On the iPhone got to Settings > iTunes and Apps Stores and make sure "use cellular data" is set to ON.

You're welcome.

Ok, I bought 3000 songs to be ON MY iPHONE, not IN THE CLOUD. How do I get them downloaded ONTO my iPhone so I can play them anywhere, in the car, through a PA or stereo, wherever? I just upgraded from iPhone 4 to 6S. Didn't have an issue with the 4, don't know if it was on " use cellure data". Won't that cost me download data to play from icloud?

FINALLY!

Someone who understands my problem!

Why does Apple have to control everything? They say it is "helping" us, or it increases "ease of use".

Apple has become what they originally were fighting against-- a Goliath corporation controlling as much technology as possible.

Any Davids out there willing to go up against them?