iPhone5 turns on until Apple logo and then turns itself off automatically. Any way to solve this problem?

Hey cristinaglez,

Thanks for the question. The following resource provides information about the symptom you are experiencing:

iOS: Not responding or does not turn on

http://support.apple.com/kb/TS3281

Symptoms

Your iPhone, iPad, or iPod touch may occasionally stop responding to buttons, switches, or touchscreen input and may exhibit one or more of these symptoms:

[…] - Does not start up past Apple logo

Resolution

1. If a single application is not responding or stops responding when it opens, you can force it to close.

2. If the device is unresponsive or if certain controls aren't working as expected, restart your device.

3. If the device remains unresponsive or does not turn on (or power on), reset your device.

4. If there is no video or if the screen remains black, verify that the device has enough charge to turn on:

1. If you are using an iPad, ensure that it's connected to the USB Power Adapter supplied with the device.

2. Let it charge for at least twenty minutes, then see if it starts normally.

3. If there is no image on the screen, press the Sleep/Wake button to attempt to wake the device.

4. If the screen displays a red battery icon, continue charging the device until the battery is fully charged. Learn more about charging iPhone and iPod touch, or iPad.

5. If the above steps do not resolve the issue, or the if the screen remains black or shows a persistent Apple logo, try restoring with iTunes:

1. Connect the device to your computer and open iTunes.

2. If the device appears in iTunes, select and click Restore on the Summary pane. Learn more about restoring iOS software.

3. If the device doesn't appear in iTunes, try to force the device into recovery mode, and then restore it.

6. If the above steps do not resolve the issue, contact Apple.

Thanks,

Matt M.

i try to restore my device on itunes it just goes back to the screen that said connect to itunes