Q: My iphone 5 is frozen, yet I'm able to restarting it

Try to reset your device. This won't delete your data stored on this device.

• Press and hold the Sleep/Wake button
• Press and hold on the Home button
• Keep holding both buttons until the display turns off and back on with Apple logo on it.

If your iPhone, iPad, or iPod touch won't turn on - Apple Support

If this does not help, restore your device to factory settings. Note that this will erase the data from your device.

Take a look this Apple Support article: Use iTunes to restore your iPhone, iPad, or iPod to factory settings - Apple Support.

Have you checked all the steps suggested in the article?

If your phone is showing the iTunes icon and cable image then it's gone into recovery mode. You have an up-to-date version of iTunes installed on your PC, does that recognise the phone when you connect it ? If it does then it should recognise that the phone's in recovery mode and let you reset the phone, and you can then restore/resync your content to it

You can, or you could install iTunes on your PC (http://www.apple.com/itunes/download/). If the Mac is the computer that you sync the phone, and have your backup and/or content on it, that would be the better computer to use