If you picked up a new iPhone 5, did your iCloud, and something's still missing, you might have to move the data over manually. Likewise, if you set your iPhone 5 up as a new device but still want to keep data from a few apps or games, you'll have to move it over manually. iCloud and iTunes are great, but they're not granular.
If you use a Mac, an app like Ecamm's PhoneView is an excellent option. It'll let you browser your old iOS device, copy off just the data you want, and then copy it back to your new iPhone 5. And it's fairly straightforward to do.
Disclaimer: Moving files on your iPhone, or any iOS device for that matter without knowing what you're doing or where you're dropping files can corrupt your file system. Before moving anything, be sure it's what you need to move and that you're putting it in the right location. If you're unsure, we wouldn't recommend proceeding any further.
Note: Our directions are for Mac users using PhoneView but there are many other apps you can choose from in order to pull data off for both Mac and PC. The layout may be different but the process should be similar.
In order to transfer data from one iPhone to another you'll need a few things:
PhoneView does offer a free trial but what you can pull off your device may be limited. We recommend buying it if you want to make sure you're recovering all your data. Then if you ever need it again, you've already got it.
Once you've made sure you're good to go with all of the above, you can move on.
That's it. The next time you launch your app or game on your iPhone 5, it should be just like you left it on your old iPhone.