How to transfer My iphone 3 apps with all its data to my new iphone 5?

I have some games that i bought on my iphone 3. And they still have progress in them, also i paid for some special stuff on there so i don't want to loose any data.
Is there a good and safe way on transferring apps from your old phone to your new one?
I looked at a lot of stuff online but either they don't make sense, or they are using i cloud and my iphone 3 doesn't have icloud and i'm scared to update it so it can have it because last time i updated my iphone everything was deleted.
I also tried this iexplorer method, but after i updated my itunes it stopped working, so i'm stuck.
Someone help? Is there a way to transfer my apps and their data to my new phone so theyll have everything on there.

I'm not sure if its 100% safe to update your iphone 3 yet (depending what version your already on) to get icloud on it. But i think you can go to an Apple Store like in a mall and have them do it for you.