Busted Verizon Galaxy Note 5 screen, trying to use adb to unlock
You can use CWM or Philz Touch recovery to make a full backup by just using the volume/power buttons.
You can also use an OTG adapter and a USB mouse/keyboard to interact with the phone. If you can't see the screen either, you can use a MHL to HDMI adapter to hook up your screen output to the TV. You may or may not be able to use an OTG mouse or keyboard daisy-chained to the MHL adapter (depends on MHL adapter, unbranded one didn't work for me).
If your bootloader is locked and MHL+mouse idea doesn't work out, your best bet is to get the phone fixed. I would recommend to buy a second phone with Bad ESN off ebay, and just swap the motherboards, with the amount of damage you have. Then you can resell the leftover parts.