It seems that Nexus 5 ships with Hangouts as the default (only) app for SMS messaging but I'm not interested in Hangouts and I prefer the messaging app I had on my Galaxy Nexus.
How do I get the Galaxy Nexus Messaging App onto my Nexus 5?
You're not alone in wanting the old Messaging app!
Even though the old stock Messaging app is no longer included in Android, you always have the option of installing an alternative. In fact, people are recommending 8sms as a replacement for Hangouts that is almost identical to the original stock Messaging app. In fact, it is built from the source code of the original Messaging app, with "some enhancements".
Your best bet will be a third party solution as Google is attempting to consolidate many of their services and apps together for a more streamlined approach. I can understand not wanting to muck with Google messaging when all you want to do is send SMS, but that's the way they are headed with Hangouts being the Messaging app.
Now, if your Nexus 5 is updated to Android 5.0+ you can use this new Messenger app from Google.