Make sure youe updat your 5s. The only way it could be incompatible with the backup of your old phone is if it was running a lower version of iOS. Update the 5s and try again.
If that doesn't work, back up your iPhone 4 to your computer instead. Connect it to your computer, open iTunes, then go to File>Devices>Back Up. Then go to File>Devices>Transfer Purchases. When setting up your new phone choose Restore from iTuens Backup and restore the backup you just made to your 5s.