Congrats on the shiny new iPhone 5. I have the same camera in my iPhone 4s (did you know they had the same camera?) and use it non-stop, with the result that I too have a ton of photos, typically hundreds upon hundreds of photographs, all stuck in my own "Camera Roll" album in the Photos app. Annoying.

You can certainly add new albums to organize things better, but here's the downside: for albums that are based within your iOS device -- whether it's an iPad or iPhone -- the photos are linked to the new album and still stay in the Camera Roll too. So you can't "move" things around and the albums really end up being more of a keyword organizational tool.

Still, it is useful, so let me show you quickly how to add a new album to the Photos app and how to then link some of your pics -- and they can be in any other album, they aren't constrained to just be in "Camera Roll" -- to help organize things!

First off, tap on "Photos" and you'll see something like this:

Notice that I already have some additional albums, "Cute" and "☆ ☆ ☆ ☆ ☆". Those, along with the contents of "Photo Library", are all managed by Aperture on my OS X system, and the five star album is automatically expanded every time I rate a photo I took as five-stars within Aperture, so that's a nice way to keep a 'best of' album too.

To create a new iPhone / iPad photo album, however, tap on the "+" on the top left.

Give it a memorable name, and feel free to use spaces, capitalization, whatever...

You can see that "Cute" is insufficient and I need "Really Cute" too. Okay. I enter the name and tap on "Save".

Now I'm in this weird mode in Photos where anything I browse and select will be automatically linked to the new album, as you can see here:

You can go into any other album and it'll show thumbnails of everything. Tap on the group or cluster you'd like to add, move back to other albums, zip around. When you're done tagging your photographs, tap on "Done" and your new album will be built and ready to share via the slideshow feature.

To gain the capability of actually removing photos from the "Camera Roll" and having them in a different album, you'll need to use iPhoto or Aperture on your Mac to do the work. On the iPhone / iPad itself, that's just not an option.