How to transfer photos/music from iPhone 4 to new iPhone without computer?

Hi,

My iPhone 4 is incredibly slow these days and old so thinking about upgrading to a new iPhone 5s.

Is it possible to transfer all my photos from my old iPhone to a new iPhone without a computer? Sorry if there is an obvious answer but I can't find it!

I have an ipad on the same iCloud account and photo streaming is set up but as I brought this more recently, only some of my photos are on the ipad. Older ones are not.

Any suggestions would be much appreciated!

Thank you!