Fiona,
The correct path here is to open a tech support webcase, same as described in http://www.adobe.com/go/kb405200. Supply the email address used for your Adobe ID and we'll reset your activations.
Now, what might be happening here is that your PRS is authorized to a different Adobe ID than your copy of Digital Editions. That can be a problem.
In this situation, the error message should give you the opportunity to authorize with the your Digital Editions AdobeID. But of course you have to get an activation reset first (post your case number back here)
If that fails, re-authorize Sony PRS-505 reader by pressing Ctrl+Shift+E. (there is no support for Sony-PRS505 on Mac, so no Mac OS equivalent shortcut is possible).
This will deauthorize and should ask you to authorize again. If the you're not asked to authorize again, they unplug and replug the Sony PRS-505 Reader and Digital Editions will ask to authorize the Reader when it finds it again.