What everyone else said is correct.
This happens with almost every phone, it's a default setting in the youtube app.
I used to have the Droid X2 before the iP5 and when watching videos the youtube app will load it according to your connection. If your connection is 3g or less, it will not play in the highest quality, instead it'll adjust to a lower quality so that your video doesn't stay buffering. But if you watch the same content over WiFi, or LTE (assuming your LTE speeds are fast), it'll load with the highest quality.
On the Droid X2 you can go into the settings of youtube and there was an option to load all videos in the highest quality regardless of connection speed. Not sure if there's one for the iP5. Like I said, I'm new to iP5 and still messing around with it.
I just learned how to charge the iP5...jk