Here's another
youtube video of a PRS-505 battery replacement. I saved the link because I noticed his care in taking off and putting on the metal case.
eBay US has similar battery listings that state they fit both the 500 or 505. Some listings are only for the 505, but those batteries look identical and have the same part number as the other 500/505 listings.
Here's
a thread where some emphasized the care needed with the ribbon cable.
Good luck!