Welcome to the forum! Who is your carrier, what is the model of your device? Just an FYI: The radios listed in the OP are specifically for Verizon model SM-N900V.
You do not need to be rooted for this particular method, BUT, this is specifically for Kit Kat and you're currently running Lollipop. If I'm not mistaken, once you've taken the 5.0 update, you cannot downgrade to an older version. (Hopefully someone can verify the same with the radio/modem)
When did you upgrade your device to 5.0? Did your reception problems start after talking the upgrade? Did you do a factory data reset after taking the update? Personally I would go that route first. A FDR is always advised after taking a major update like this. Especially on older devices.
Upgrading or downgrading your baseband firmware or radio will not always give you better reception, and in certain situations, can actually make it worse. I would try doing a FDR first.
Hang in there and hopefully one of our current or previous Note 3 owners can provide some more insight.
I have Verizon Samsung Note 3 SM-N900V running 5.0 with baseband n900vvrueof1, bought the phone off my wifes friend to upgrade my work phone that was an iPhone 4s. I hate I-everything and love the android systems. As soon as I activated the phone it did 4 upgrades from 4.3 ending on 5.0 so I am not sure what service it was getting prior to the upgrade. every other Verizon phone that has been at my house gets nearly a full signal on 3g granted the Note 3 is 4g lte I would assume having the ability to switch to 3g and 1x I should hold some signal. I end up going from 4g lte 2-3 bars to 3g 1 bar to 1x 2-3 and no signal without even moving at times even showing 3g or 4g bars and as soon as I hit send on a message it says No Mobile Network and wont send. I did do a full factory reset today and have still been spotty on signal. figured changing baseband helped with my galaxy s4 previously so I might would give that a shot if I could at this point
S5 tap'n