Not sure if you'll have to do this on Nexus 5, but I had to explicitly specify my device info to get Sprint Zone fully working on my Nexus S.
In the following file...
/data/data/com.sprint.zome/shared_preferences/com.sprint.zone_preferences.xml
...I added the following lines...
<string name="funnyPref1">%NAI%</string>
<string name="funnyPref2">%MEID-HEX%</string>
<string name="funnyPref3">%RESELLER-ID%</string>
<string name="funnyPref4">%MSID%</string>
<string name="funnyPref5">%PRL-VERSION%</string>
<string name="funnyPref6">%MDN%</string>
<string name="funnyPref7">%MAKE%</string>
<string name="funnyPref8">%MODEL%</string>
...with my actual device data, of course. It looked something like this:
<string name="funnyPref1">jason****@sprintpcs.com</string>
<string name="funnyPref2">A00000**********</string>
<string name="funnyPref3">Sprint</string>
<string name="funnyPref4">504*******</string>
<string name="funnyPref5">60798</string>
<string name="funnyPref6">504*******</string>
<string name="funnyPref7">Samsung</string>
<string name="funnyPref8">Nexus S 4G</string>
Prior to doing that, tapping Refresh would spit an error into the device log stating "mdn is a required parameter," which is what the server responds when it doesn't receive a valid MDN. After making the modification, account auto-login worked correctly, I could see all my devices and billing data, and service trender alerts appeared.
This seems to be an issue because my device doesn't system properties for MDN, NAI, and PRL that Sprint Zone is looking for. I've been attempting to reverse-engineer the specific properties with no success. I'll post them here if I can find them, since using setprop is a lot easier than modifying shared preferences.