If you have the 'Backup my data' option checked, it should -- though it is half baked and doesn't always work.
When you're signing into your Google account on the N5, you should see an option that says 'automatically restore my data' or something similarly worded. Just make sure you check that and connect to WiFi during the setup.
You could also backup your apps/data to your computer (or even Google drive) with something like Helium to be on the safe side.
Found 'backup my data'. It's checked. So that should be enough? Sign into my N5 and the apps will download automatically? Maybe look into helium?