I doubt anyone in this forum can give you the definitive answer on that, probably just bad news that you should have used the trial before buying, etc.... though I may be wrong.
I don't believe Adobe sells previous versions, so you may not be able to buy the older version thru them. As far as getting a refund, I don't know if that's possible either, but the folks who will know/decide that are the ones you need to talk with.
Try starting with chat and see if someone there can direct you to a better contact... http://www.adobe.com/support/chat/ivrchat.html
If your hardware can run it, it's may be cheaper to upgrade your OSX 10.5.8 to Snow Leopard then to Mountain Lion 10.8.
The Mountain Lion upgrade apprently requires Snow Leopard first.
Ned is correct we do not offer Photoshop Elements 10 for sale any longer. I would recommend following John's suggestions to see if you can upgrade your computer. If not then you may want to request a refund.