[Verizon Galaxy S 5 General] oxygenwater1988@yahoo.com:
Awesome, I was able to root my device with that archive, thanks (more info below for other people going through the same thing).

That archive had eight apks, none of them named (I'm guessing for obfuscation purposes). I uploaded all of them to my device and the 8th one (about 100kb) was towelroot. It was a little different than the standard towelroot, because it had a green lambda instead of the orange lambda. However, unfortunately it was still v3. And I got the same error message "Please ensure you are connected to the internet." I could not find a secondary towelroot apk anywhere in the archive (ran a search for apk to double check).

I have a CID 11 device but decided to try the instructions in that thread you sent. I ran Kingroot, and it seems to require an internet connection as well. However, this app seems to actually be able to connect online and find a "strategy." It was a one-button operation, so once it scanned my device model I clicked root and it ran up to 83% and then stopped. Kingroot said "3 issues need attention," and had an "optimize" button. I clicked it and it seemed to make changes to my device before continuing up to 94%. Then it stopped again before needing me to click some more things. I optimized as much as I could but got stuck at 97%, with one final task left. It was called "Purify" and when I tried to enable it, I got a "Start Failed" error message. After looking more into this, it seems like an optional battery feature. I gave up on Purify and went to the main tab of KingRoot and saw the status "Root successfully."

After rooting my device, I was able to follow the rest of the guide. My experience below.

Was able to grant root privilege to Superuser, Busybox, and Safestrap.

Unfortunately with Superuser I am unable to follow the steps to install the binary normally. It says that the SU binary needs to be updated, and when I click continue, it gives me the option to install the SU binary normally or via TWRP/CWM. I click Normal and after showing an installation prompt for a few minutes, it fails with the error message "Installation failed! Please reboot and try again." After a reboot I get the same error message, tried three times. I realized that the steps said I could skip this step. I had no choice but to do so.

Busybox installed successfully!

Safestrap installed recovery successfully. However, the option to reboot into recovery was grayed out. I rebooted and it remained grayed out. I decided to try the Safestrap apk that was in the thread you linked me (VZE EMMC 15 thread). This Safestrap apk was a little different, it had a blue icon instead of a green one. With the blue Safestrap I was able to install again, but this time reboot into recovery was not grayed out. I was able to reboot into recovery.

Within Safestrap I swiped to allow modifications. I followed step 14 and chose Dalvik, Data, Cache, and System. Then I followed step 15 and flashed Lollipop (ChooseEMMC_11_PB1_LL_STOCK_SAFESTRAP_ONLY.zip). The flash succeeded. There's an option to install TWRP when rebooting. The instructions seemed to imply I could skip this so I clicked Do Not Install and the device rebooted.

Unfortunately, my device now does not seem to be able to boot. It is stuck at the Samsung Galaxy S5 splash screen.