Hi jilliewis,
Should be reasonably straightforward as long as you make sure that you keep the same Adobe ID.
First thing I'd do is download the latest version of the Reader software from Sony's website on to the new computer: (http://www.sony.co.uk/support/en/product/PRS-505/downloads/SWupdate_Reader_PC_v1_11230).
You then need to authorise the new computer with your Adobe ID - it is essential that you use the same Adobe ID (usually an e-mail address) and password as you used for your old computer (if you can't remember go to the old Reader Library software on your old computer and look under 'Help' and then 'About Reader Library' - here you should find a message that tells you that this PC is authorised and the e-mail address that was used .... can't help with the password though!) To actually authorise the new computer, this happens automatically when you buy a copy-protected eBook. If you don't need to buy a new eBook at the moment, you might be able to re-download something you've purchased previously if you visit the purchase history section of any websites you've used to buy eBooks - some will let you do this. Either way, press the 'download' button on a store's website and choose the 'open' (not save) option when prompted. This will automatically transfer the eBook onto your computer and you should see the prompt to enter your Adobe ID and password that will then authorise your computer.
The software on the new computer will automatically recognise your PRS-505 when you connect it, and as the Adobe ID should match the authorisation from before then you will be able to transfer eBooks between the new computer and the Reader as before which includes transferring from the Reader to the computer. Click on 'Reader' along the top of the new Reader for PC software which will display the eBooks stored on your Reader. Select any that you want to transfer onto the new computer and press the 'Copy to My Library' at the bottom left. This I think is the easiest way of transferring your library onto the new computer - just make sure you have everything that you want to copy transferred onto the PRS-505 from your old computer.
Sorry for the long explanation, but hope this helps:smileyhappy:
