Your post is a bit unclear about what you are doing ("hook up to computer" how, what information can you get on your computer screen, even where you are trying to "select transfer"). Are you trying to do a file transfer with a dead screen, or have you managed to mirror the screen? If the latter, does the touchscreen work (this may work even if the display doesn't)?
If not, you can interact using a wired mouse or keyboard and a USB OTG adapter, and if you can get the screen mirrored (I don't recall what mirroring options the Note 5 supports) plus that then you are sorted: that would let you control the phone while mirroring the screen via USB, and hence manage a cloud backup, WiFi backup or whatever. But if you can only mirror through the USB port then you'd not be able to see what you are doing while using wired input devices, so a lot of trial and error would be required (I managed this once with a broken HTC M9, but it took time and patience...).