iPhone 5s stuck in recovery mode

"Alright. Error 4013 sounds like a nand issue. Likely cold solder joint. Let's try Mohammadali's approach. You could remove the pentelope screws, carefully remove the home button clasp and cable, then remove the two screws on the battery plate, then disconnect the battery, reconnect and carefully re apply everything. Also, while doing this. Be careful of the display cables at the top. Make sure they are always close, so as not to damage them. Then try putting the phone into dfu mode. Here's a guide for the phone, and I'll post steps to put phone into dfu mode

How to replace the battery in your iPhone 5s

Remember, you don't need to take the whole battery out. Just remove cable. Replace cable

Plug your device into your computer with a USB cable.

Turn off the device.

Hold the Power button for 3 seconds.

Hold the Home and Power buttons for 10 seconds.

Release the Power button but keep holding the Home button.

Here's some steps to try to get your phone into dfu mode. Also can you tell us what happened? Why are you trying to restore it? Was there damage? Water?"

Try to open the phone by taking the two bottom screws off and then unplugging the battery and then putting it back on. Do at your own risk. You can also try to hold the home button and the power button at the same time for about 40 seconds while plugged into the outlet and that may also make it work.

"Try to restore with 3U Tools and use with other lightning cable. Another option if still failed, as Imedic say's if the problem is cold soldering, you can heated iphone at back case, and while its still warm, try to restore

EDIT

Please read this thread

iPhone 5S Stuck in recovery mode : iTunes restore error 50"

I had turned my iPhone 5s off because it was acting slow. So I had turned it off then it restarted my whole iPhone and now I cant get back in it and also i cant update it