error code 1671 could not be found in error code list where as error code 1671 is thrown in message box while restoring my Iphone5

As a final step you can try the DFU mode. This will download the latest software version on your device.

• Connect your device to your computer using a USB cable.
• Turn off the device.
• Press and hold the Power button for 3 seconds
• Press the Home button while holding the Power button and hold both for 10 seconds.
• Release the Power button, but KEEP HOLDING the Home button.
• After about 15 seconds, iTunes will tell you it has detected a device in Recovery Mode.
• Restore your device

More info here: https://www.theiphonewiki.com/wiki/DFU_Mode

This subject was tackled by one of our senior contributors In a recent question. Here is the link, and you should check out the reply by IIIaass.

https://discussions.apple.com/thread/7176628

I want to thank you!. You saved me over $100. Just to review my iPhone 5S the charge was $50 and to upload the Operating System they charged $60. I just downloaded the IOS once I did your instructions to the letter. The file to download is 3.8GB and now I have my iPhone back. At the Shop they told me that my USB port on the device it was an additional $60 and that there was the provability that the mother board was damaged...
I want to thank you for your valuable post.

Thanks and regards

aaraya57