mobile

I have a Verizon Samsung Galaxy S5, SM-G900V, running Android 4.4.4. I accidentally ran a factory restore, wiping out my files. I want to try to get the data off of it, since the files may not yet be overwritten, but I have no idea of how to go about this, especially using a method that does as few writes to the internal memory as possible (to increase the chance of success). I would very much rather not root, or at the very least not trip Knox or otherwise void my warranty. However, I might be willing to risk it if necessary. I have never rooted before, and it seems as though rooting utilities have a difficult time with this phone (at least in part thanks to Verizon).

I have not found any guide on how to do data recovery in this situation. I've tried at least one recovery program that was completely useless, though that might be due to lack of root. I am familiar with computers, and Linux, but Android is very foreign to me, and it seems like most data recovery attempts require me to mount the device on a computer as a disk drive. Although I've gotten it to connect for file browsing and transfers, I have not managed to get a connection where it acts like a mountable, normal disk. Naturally this rules out getting a memory image with this method, leaving me rather stranded.

Can anyone provide me with some assistance? I'm not expecting to fully restore the phone, but I've got some files (especially the memo and contacts) I'd rather not say goodbye to since my last backup.

Any assistance would be greatly appreciated. Thank you.