Congratulations on your new iPhone 5s! And thank you for providing the details of the issue you are experiencing when restoring your iCloud backup. iCloud backups can take quite a bit of time to restore:
The restore process is taking a long time to finish.
Even with a fast Internet connection, the restore process may need 1 to 4 hours per gigabyte to complete.
If you are still encountering the same issue, it may be that the restoral of the iCloud backup was interupted. You may want to restart the process. I recommend restarting it before you go to sleep so that it can complete through the night.
Thank you for using Apple Support Communities.