The exact same thing happened to me, pretty much on the same day as you. I roamed with an international SIM for a while, and couldn't connect to Sprint voice when I came back.
Sprint was zero help, since there are so few of these on the Sprint network they never see this problem.
After 10 hours on the phone and in the store with Sprint, I finally found the solution myself. You have this problem:
https://productforums.google.com/forum/m/#!topic/nexus/Or6_6zCtBwc
It's a known bug in the CDMA radio stack of Android 4.4.4, and even a factory reset won't help. Your choices are a new phone (they'll replace it under warranty or TEP or charge you 75 bucks) or reflash it yourself. Sprint stores can't reflash the firmware, so you're on your own. It's actually not that hard.
Some folks on the Google forum thought clearing out the APN settings would work, but they didn't for me. You could try that before doing the drastic stuff.
Back up your phone, write down your MDN and MSID, reflash back to 4.4.3 or 4.4.2, and put the Sprint SIM back in. You may need to have customer care or the website self-service reactivate it like it's a new phone. Once it reboots, it'll update back to 4.4.4 over-the-air.
Sound difficult? The WugFresh Nexus toolkit almost makes this a one-click process:
Nexus Root Toolkit v1.8.6 | WugFresh
I'd be lost without that toolkit. Even if you get them to replace the phone, you'll want to use the NRT to back up the old one first.
In the end, you'll have an unlocked rooted Nexus 5 to show for your troubles. I know it sounds ridiculous that you have to go through all this just because you swapped your SIM card, but it's Google's fault for not adequately testing 4.4.4 before foisting it on the six of us who use the N5 on Sprint.
--Qfg