According to the PSR-400/PSR-500 Owner's Guide, they use the PA-5 power adapter, which is discontinued. The Yamaha web site doesn't list the specifications for the PA-5 power adapter, but does have a picture of it which, when enlarged, shows "OUTPUT: DC12V 1.5A"-- it's a little blurry, but that agrees with the description of the PA-5 that can be found in the PSR-500M Owner's Guide. So it sounds like the power adapter you were given with the PSR-500 was slightly out-of-spec from the preferred adapter. However, the Specifications on page 40 of the PSR-400/PSR-500 Owner's Guide says that the "Rated Voltage" is "DC 9~12V," so I guess the power adapter you were given was within the instrument's tolerance.
If you want to get something with the same specs as the old PA-5, you can get the PA150 power adapter from Yamaha, which replaces the old PA-5. Your local Yamaha dealer may have one, or you can order a PA150 or PA150MM from Amazon (the PA150MM seems to be the same as the PA150 but costs less for some reason).
Edit: PS-- If you don't already have a pair of headphones and a foot controller for the PSR-500, and if you don't mind spending a little more money, then you might want to consider getting the SKD2 Survival Kit rather than just a power adapter, since it includes the PA150 power adapter, the FC5 foot switch, and a pair of stereo headphones. The headphones are cheap plastic and shouldn't be handled roughly or they might break, but they're comfortable, sound okay, and most importantly they have the larger-size audio plug that's required for the keyboard (most headphones these days have the smaller-size audio plug that fits the audio-in jacks on most computers) so that means you won't have to buy an audio adapter for the plug. And the foot switch lets you turn sustain on or off-- it isn't nearly as nice as the FC4 foot pedal, but it does the job.