There may be a directly-odin flashable way; I don't know. It sure seems like there ought to be; Google it, cunt. ;)
The waters here are murky for me because I'm on Verizon, so I'm blessed with a locked bootloader and therefore none of the cool kids like to play with me. If it were unlocked, I'd probably just install cyanogenmod and call it done.
But the downgrade, as I understand it, is needed because towelroot is needed because, well, it's VZW. And the security exploit that towelroot uses (thanks, geohot!) got fixed a few short months into the S5's life.
The downgrade is also needed because safestrap is awesome (thanks, Hashcode!), but won't run on newer kernels: It still does its thing, with multiple ROM slots and magical flashing of zip files, but its GUI becomes borked.
This can allegedly be done all on-device, once rooted, with flashfire (thanks, chainfire!), but I haven't bothered with that yet. (And remember, the first rooting requires towelroot which requires old firmware....)
And since that's the method that I learned when a buddy got an S5 last year, which I repeated when I picked up an S5 a bit later, and which I repeated -again- recently when my previous S5 drowned (IP65 my ass), that's the one I write about.
I do not pretend to be an expert on the topic, just someone who has successfully navigated the waters a few times.