Can I stream HD videos through LTE or 4G on my iPhone 5?

When I had Internet at home and connected to Wi-Fi, the HD videos I streamed (Netflix for example) on my iPhone 5 streamed just fine in HD but if I use LTE or 4G they didn't stream in HD, is there a way around this? I have unlimited data through AT&T and I know that AT&T does this on purpose regardless of data plans so phones don't use as much data but I don't have Internet at home right now and I really want to watch HD movies through my iPhone 5 that's connected to my tv through the HDMI adapter.

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