Iphone 5s is having problems with update?

I tried updating my iphone 5s everything was going smoothly till my phone kept turning off and when I would turn it on again the little usb cable with the itunes sign was there and I had to keep trying to update it over and over again and my phone just won't stay on and the battery percentage is at 80 so its not a battery problem. Not sure what is wrong but its frustrating because now I can't use my iPhone since all that is on the screen is USB cable. What do you guys recommend?

Added (1). also the cable is fine its brand new but the iPhone won't stay on it keeps turning off and I turn it back on trying to use recovery mode but it only stays on for a few seconds and the usb cable is all that appears

Press and hold down the Home key for about six seconds. If this works, you are returned to the Home screen, with (hopefully) everything working again.

Its likley the firmware within the phone needs to be refreshed

how to put your iPod touch / iPhone into DFU mode. Works with all G's of iPod touch / iPhone

What is DFU: Device Firmware Upgrade

Step 1: Turn off your iPod touch / iPhone completely and connect to PC / mac

Step 2: Hold down the Power button for 3 seconds

Step 3: Without releasing the power button, also hold the Home button for 10 seconds

Step 4: Without releasing the home button, release the power button and keep holding the Home button for 20 seconds.

Itunes will identify that you are in DFU mode.

- If not successful and you can't fully turn the iOS device fully off, let the battery fully drain. After charging for an least an hour try the above again.

- Try another cable

- Try on another computer

- If still not successful that usually indicates a hardware problem and an appointment at the Genius Bar of an Apple store is in order.