Welcome to Android Central! Since you have a Nexus 4, all of your contacts should be in your Google account (rather than the local Phone account, which Nexus devices don't have). On your computer browser, go to contacts.google.com--if all of your contacts are there, then they will sync automatically with the new 5X once you log in there with your Google account.
All of your Google app data (like Calendar, Google Drive, etc.) should be synced to your Google cloud, and will therefore sync automatically with the new phone. But 3rd party apps may or may not backup data to your Google account--it's usually difficult to tell which ones do. If individual 3rd party app data is important to you, you might consider using
Helium to back it up, then restore it to the new phone.