In my opinion, it is something that's really hard to do (or that might even be impossible), that's why, sadly, I think that you are not likely to get your data back.
Most of the time, when you erase some data on a storing device, actually, you don't really erase it but just hide it and give to the devices using it the authorization of writing on it, that's why, in some cases, you can get your data back.
Unfortunately, in your case, that's something much more complex for several reasons.
The first one is that getting back the data in the way I mentioned above needs to have an access to the storage at a pretty low level. Apple putted some restrictions on the iOS devices and for this reason I don't see any way to gain such a low level access without doing something dangerous and not allowed by Apple such as jaillbreaking your device (and even with this I'm not even sure you could gain this access).
The second one is that since you transferred some content from your iPhone 4s to your iPhone 5s, it might be possible that the photos have been replaced by some new content (so some or even all of your photos might be missing/corrupted).
The last one — which might be the biggest one — is that the storage is managed in a pretty special way in iOS for some security reasons and although I don't know what happens exactly when you restore you device, it might be possible that iOS protects the previous content by removing some keys that were encrypting your data, making it nearly (not to say completely) impossible to get it back.