Is my Nexus 5 supposed to be this shitty?

Picked up a Nexus 5 from the Google Play Store last week to save myself from iOS, and while I'm so happy to be back with an Android device, I am really blown away by how terrible of a phone the N5 is proving itself to be.

Primary issue is that the phone can't seem to hold a signal for longer than a minute at a time, if it can even find one at all. I'm using Tmo in LA and I typically have amazing service all over the city. This is the first device I've had any network issues with at all since switching carriers a few years ago, in fact.

Because of the endless network search, my battery lasts around 5-6 hours, max. It's insane. I can hardly connect to instagram long enough to refresh my feed, and then the battery is toast by 1:00-3:00 pm.

Does anyone else on here have a Nexus 5 with issues like this? What steps should I take to resolve this? If anyone has any solid advice, I'd definitely appreciate it. Don't want to have to return this phone as I really do love using it.

...just wish it worked properly -_-