[Samsung Galaxy S5 Neo Questions & Answers] Justin_B:
I'm new to root as well, but I just rooted my own S5 Neo (which is why I saw your post while searching for information), so I'm a couple of weeks ahead of you.

I'm a little unclear why after flashing TWRP you say the root check confirmed root. My understanding is that TWRP alone won't root the phone.

You may have already figured this out, but here's what I needed to do to install TWRP and Magisk. The issue for me was that auto-reboot from ODIN was allowing the phone to clear TWRP before it was installed. I'm not sure what your issue is, but there is one possibility I note below.

My successful procedure follows (ask for clarification if I gloss over something you don't understand). Others should feel free to correct any mistakes I write, since I'm no expert and I'm writing from memory:

1) Download the Magisk ZIP to your phone, so it will be available when needed.

2) Ensure your phone is set for OEM Unlock (via the Settings/Developer Options setting menu, which is only shown after you activate it by going to Settings/About Phone/Software Information and tapping Build number 7 times).

3) Download the TWRP *.img.tar file to your PC. Make sure it was made for your model phone.

4) Start ODIN on your PC, and use the AP button to load the TWRP *.img.tar file. Wait for ODIN to finish checking it.

5) In ODIN's Options tab, unselect "auto reboot", so your phone won't reboot when done.

6) Turn off your phone, then boot into Download mode (vol_down+home+power button) and confirm with vol_up button.

7) Now connect the phone to the PC with a USB cable and confirm that the "Added!" message shows in ODIN.

8) Click Start in ODIN to flash TWRP to your phone. Wait for the top left to show a green PASS message.

9) At this point, your phone is connected and still in Download mode. Detach the cable and hold Vol_down+power until your phone shuts off (maybe 10-20 sec).

10) Boot into Recovery mode (vol_up+home+power). The phone should now be installing TWRP. Wait until it finishes and then shows something.

11) My memory here is fuzzy. I don't recall whether TWRP immediately shows now, or if the phone boots normally, or it asks you whether to boot or shutdown, so here are five possible routes:

11a) If the phone shows the TWRP window, go to step 12. I think this is what should happen.

11b) If the phone shuts off, boot into Recovery mode again. This should now be TWRP, so go to 12.

11c) If the phone boots normally, shut it off and boot into Recovery mode. This should now be TWRP, so go to 12.

11d) If the phone asks you what to do, select power off and then boot into Recovery mode. This should now be TWRP, so go to 12.

11e) If booting into Recovery doesn't show TWRP, then something is not quite right with my instructions, or how you followed them, so come back here with the results.

12) Here's where your issue may be. TWRP is installed temporarily by default, and restarting the phone will overwrite it. During this temporary time, you can immediately flash a Zip, then reboot and get your original stock recovery back. You may have restarted the phone without realizing this, which then overwrote TWRP. So you need to decide whether your want it temporarily to flash Magisk, or keep it permanent for other uses (like making Nandroid backups). To make the choice, TWRP asks you whether your want to "Keep Read Only" mode (temporary) or not (permanent).

13) If TWRP is temporary, you need to install Magisk now before rebooting. If it's permanent, you can reboot and do it later. In the TWRP menu, tap Install. Navigate to the location where you placed the Magisk ZIP. If you don't see it, look at the lower right button. If it says "Install Image", it should be showing available Zips. If it says "Install Zip", then it's showing images, so tap it to show Zips.

14) Select the Magisk Zip and it should be installed. Go back to the main TWRP menus and tap Reboot, then System to restart your phone.

15) Look in your Apps for the Magisk Manager. It should have been installed from the Zip. Open it and check that "Installed Version" has a green check. That should be it.