my iPhone 5 froze when it was updating ios7

Hi Cassandratoday2013,

Welcome to the Support Communities! The article below will help you troubleshoot the issue you are having updating your iPhone:

iOS: Apple logo with progress bar after updating or restoring from backup

http://support.apple.com/kb/TS3681

After you update iOS, restore from a backup, or erase your iPhone, iPad, or iPod touch, your device displays the Apple logo with a progress bar.

When this occurs, the progress bar might be moving very slowly or seem like it isn't moving.

If you're updating over the air, connect your device to a power source so that it won't run out of power during this process. If your device runs out of power, connect it to a power source and turn on the device to let the update or restore complete. In some cases, you may see the progress bar complete, then start again.

iOS: Not responding or does not turn on

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

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.

If you can't update or restore your iOS device

http://support.apple.com/kb/ht1808

Use recovery mode

Recovery mode erases your device and restores it, which should resolve the issue. If you previously synced with iTunes or iCloud, you may be able to restore from your backup after recovery.

1. Turn off your device. If you can't turn it off, press and hold the Sleep/Wake and Home buttons at the same time and wait a few seconds for it to turn off.
2. Plug the device's USB cable into your computer only.
3. Hold down the device's Home button as you connect the USB cable to it.
4. When you see the Connect to iTunes screen, release the Home button. If you don't see this screen, try steps 1 through 3 one more time.
   iTunes should open and display a message such as: "iTunes has detected an iPhone in recovery mode. You must restore this iPhone before it can be used with iTunes."
5. Use iTunes to restore your device.

If you don't see your device in iTunes, follow these steps for Mac or these for Windows.

Additional Information

If you started your device in recovery mode by mistake, restart it to exit recovery mode. Or you can just wait—after 15 minutes the device will exit recovery mode by itself.

I hope this information helps ....

- Judy