Even though the file is only 500MB, Photoshop loads the entire image in RAM as an uncompressed file (as if it were a completely uncompressed file). Has to do with how PS manages memory. So the file takes up 200MB for what you can see on your screen and 7GB in RAM. Best bet is to raise the amount of RAM and scratch disk space photoshop requires OR, if you are okay with it, lower your number of undos (default is 20, I think). Crop should be fairly simple, but it needs to retain the entire image (pre-crop) in your undo history which is what's taking up so much space, I'm sure. Also, try saving at each step so you don't need to store as much in one go.
I used to run into this all the time when I was dealing with huge layered images for catalogs and such. Lemme know if this helps.