Tutorial: Step-by-Step instructions on How to Root a Stock Android 6.0.1 Galaxy S5.

I just updated my stock Sprint Galaxy S5 from stock Android 5.0 to stock Android 6.0.1 by accepting Sprint's over-the-air (OTA) update, and rooted it (thanks to djxn40, the devs, et al). I took notes as I rooted in order to create step-by-step instructions that may help others. I offer these instructions with absolutely no warranty of fitness. Following these instructions could destroy your phone, the planet, and possibly even the solar system.

Step-by-Step Instructions for Rooting a Stock Sprint Android 6.0.1 Galaxy S5.

1. Install the stock Sprint Android 6.0.1 update, if you haven't already done so. You can do this by accepting Sprint's over-the-air (OTA) update if Sprint pushed it to your phone. Or you can "pull" it from Sprint by going into Settings/System Update and selecting "Download updates manually".) After installation, the phone reboots and an animation of meshing gears spins, for up to about 10 minutes. If you're connected to a PC via USB, then after it finishes installing you'll get a message about needing to install Samsung Smart Start and having to disconnect/reconnect. PC users should just be able to disconnect & reconnect the USB cable from the PC to the phone, and thereby cause the PC to install the new driver via Windows Update (assuming the PC is Internet-connected). After the new USB driver is installed, you may be prompted to allow access to the new MTP connection. Allow it. Google Play Services will need to be updated and may do so on its own or you may have to help it along. You should be prompted to reboot after Google Play Services updates. Reboot it. You'll be asked to allow access to device data for an MTP connection. Allow it.
2. Install Samsung USB drivers on PC (if you haven't already done so).
3. Download Odin and unzip/extract it to your PC. (I used Odin v.3.10.7, but other versions of Odin will work.) Odin is a program that lets you push system files onto your phone.
4. On the phone settings, go into "About Device" and tap "Build number" repeatedly until it says "Developer Mode is enabled".
5. On the phone settings, go into "Developer options" and check-mark the "USB debugging" box.
6. Download to PC, the file "twrp-3.0.2-0-klte.img.tar" from HERE. (You want the .tar file, not the .img file)
7. Download to phone's SD-card (not to the phone's internal memory), "BETA-SuperSU-v2.71.zip" from HERE.
8. With the phone disconnected from the PC, launch Odin.exe on the PC.
9. With phone powered off, simultaneously press Volume-Down, Home & then Power. You have to hold them down long enough to see the "Warning!!" screen.
10. Press Volume-Up to enter "Downloading..." mode.
11. Connect phone to PC via USB. (If it's the 1st time you've done this in "Downloading" mode, then Windows will try to download the ADB Driver & Gadget Serial Driver. You'll need those drivers or else Odin won't connect.)
12. If properly connected, Odin's "ID:COM" box should show something like "0:[COM#]" in a pale-blue highlight. If not, then you can't proceed any further, so update the ADB driver & Gadget Serial driver and/or try a different USB port, and/or try a different USB cable, and/or restart the PC, and/or try a different PC.
13. From Odin, select "PDA" if the Odin version is v3.10.6 or lower. Or select "AP" if the Odin version is 3.10.7 or higher.
14. From Odin, browse to the "twrp-3.0.2-0-klte.img.tar". (Wherever you stored it in step #6 above.)
15. In the Odin "options" section, make sure "Auto Reboot" and other options are unchecked. (PDA or AP should be check-marked.)
16. From Odin, select "Start". Odin will show the downloading progress (and you'll see a progress bar on the phone's screen). Then Odin should indicate downloading success. E.g. Odin v3.10.7 displays "PASS!" in a green box when it's finished downloading.
17. After downloading is complete, disconnect the USB cable from phone and briefly remove the battery. Briefly removing the battery is easiest. Alternatively, it's possible to hold the power button down just long enough to turn-off the phone, but if you hold it a split-second too long then the phone will reboot, you'll lose TWRP, and you'll have to go back to step #16.
18. Simultaneously press Volume-Up (not Volume-Down), Home, & then Power until the phone boots into the TWRP (Team Win Recovery Project) custom recovery. If you do this correctly (and it's easy to do it incorrectly) then in the upper left corner of the Samsung splash screen, you'll see "RECOVERY BOOTING", "RECOVERY IS NOT SEANDROID ENFORCING" & "Set Warranty Bit: Recovery", and then you'll clearly see the TeamWin Recovery Project (TWRP) menu. Note that if you don't push the buttons correctly (which is easy to do) and you accidentally boot into Android or into the stock recovery, then go back to step #16.
19. From the TWRP menu, select "Install".
20. Then tap "Select Storage", choose "Micro SDCard", and hit "OK".
21. Browse to BETA-SuperSU-v2.71.zip which should be on your SD-card (from step #7) and install it.
22. Check "Reboot after install" and "Swipe to confirm Flash". When it reboots, you should see "Set Warranty Bit" in the upper left corner of the Samsung splash screen.
23. After the phone reboots, go into the app drawer. You should see "SuperSU Free" which indicates that you're most likely rooted.
24. However, you should probably double-check that you're rooted by installing a root-checker like "Root Check (by JR Rummy Apps) from the Play Store. Open it. Grant it root access (hopefully, if you're rooted). Consider optionally installing "Busy Box" from within the "Root Check" app since the Busy Box Linux-utilities are used by many root apps.
25. Profit. You can now install root apps like Titanium Backup & X-plore File Manager. And you can do a (Nandroid) "Backup" from within TWRP which I highly recommend, since it lets you restore your phone should the system software get corrupted.

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