Hello ArmyWifeCarson. Apple has a wealth of support documents that will help you in transferring your information from your iPhone 4 to your new iPhone 5s. I think you'll find this information helpful: iOS: Transferring information from your current iPhone, iPad, or iPod touch to a new device.

I want to stress to you the need to back up your iPhone 4 content with iTunes before setting up your iPhone 5s. Doing so will store all of your current data and settings so that they can be transferred to your new iPhone.

After you've set up your new iPhone 5s and restored it from the backup of your iPhone 4, all of your data and apps should be loaded onto the iPhone 5s. Sometimes, you may find that one or more of your apps are not on your phone (it's not common, but it does happen). In that situation, you can open the App Store app, tap "Purchased," and a list of all the apps you've purchased with your Apple ID will be listed. Tap the little cloud to re-download the app and your little families should still be there (mine were when I restored from backup on my iPad).

If you have used more than one AppleID to purchase content from the App Store, you may need to repeat the process for each different Apple ID.