When I wrote "it can, it can" I was refering to your question about Premiere Pro, not the elements. The CS5 version and maybe the CS4 but I'm not sure about this last one.
The issue to me with CS5 is the memory you have now.
I mean, I have it and on a computer that has exactly the same memory as yours and it's simply not working properly.
In Adobe, I have to use the CS3 to stay in the computer's power and edit at ease but this older version does not allow native AVCHD editing.
And be carefull, if you install a newer CS, you can't go backwards to previous versions. All your editing would be lost.
Keep in mind that prices of Avid MC5 and CS5 are about the same. If you are used to Premiere the natural step is to stay where you know and do not loose more time in more learning curve.
The steps are dead easy, simply do what Keith pointed on the jpeg and you're done. Import the files and ready to work.
Your issue won't be the how but the machine itself. First read well the adobe mimimum specifications for the computer and see if that's worth.
Otherwise, a lot of users would convert AVCHD to a format that you could work with.
I know Chris Sanderson works also with your camera, and if my memory does not fail, he doesn't edit in AVCHD but convert them.