from iPhone 4 to iPhone 5?

Connect your iphone 4 to itunes if you are using itunes on the same computer youve been using for itunes and not icloud as your back up. Let it back it up and sync, make sure you have all your apps and photos, etc checked to sync initunes that you want to keep. Then, after that you can connect your iphone 5 under the same apple id, and right click your phones name to the left, then click restore from backup.

iOS: How to back up - Support - Apple

Old Phone to New Phone

http://support.apple.com/kb/HT2109