My new iPhone turned off and won't turn of anymore?

So I got a new iPhone 5 today and out of nowhere it turned off and it won't turn on shake I tried everything it didn't work and if it does turn on it ll show the apple logo then the screen would go different colours then it ll turn off again please help

Was that bought straight from the apple store? Or like a second-hand?
If it is second hand, then you may be fooled about the phone. If it's straight from the apple store, try asking them to check it since they do have warranties.

Try charging the phone too.

Try to hold both the home and sleep/wake button at the same time for like 15 seconds while plugged into a computer. There should come up an itunes logo if the iPhone is not broken. From here you can turn it off and on again.

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