How can I move text messages, notes, apps from my old iphone 5 to my new iphone 5?

I recently received a new iphone 5 because my old one had completely died and wouldn't turn on. I have icloud as a back up, but hadn't done a back up since Feb. All of a sudden my old iphone has turned on and I'm in the process of backing up my data. My question is, how can I get my texts, notes, photos, voice memos, videos and apps on my new iphone? I believe only some of this information is on the cloud. I just want to restore all the same settings from my old phone to my new phone.