how to get access to my iCloud back up when setting up a new iPhone 5s which needs the newest version of iOS7 first?

Set up the new phone as a new iPhone (without using your backup), then update it to the latest iOS (7.1.2). Then go to Settings>General>Reset, tap Erase All Content and Settings, go through the setup screens again and when given the option, choose Restore from iCloud Backup and follow the prompts. This process is explained in more detail here: iCloud: Restore your iOS device from iCloud.