A simple and quick way would be to make your new Nexus 5, well, "new" again. Simply do a factory reset. Now it's just like you first opened the box and your starting over from the beginning.
Open the People app and open the contacts menu (middle option). Press menu then select contacts to display. You'll have several options. Choose the one you want to display.
If you mean they are now in your gmail contact list, go online to your gmail account and delete the ones you don't want. They will be gone when your Google accounts syncs again.