How do you correct the date on a Nexus 5?

Go into the settings menu, scroll down to date/time, you'll have the option to manually set it or have it automatically set from your network
 
If it's set to manual date, you set the date wrong. Normally you should leave it on automatic date, so it gets the date (and the time) from the nearest cell tower. If it's on automatic, I'd contact your carrier's tech support and let them know that the calendar they're using is from a different universe. (They're probably working on something, and screwed something up. It happens - they're human.)
 

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