I currently use free photo editing software; FastStone, Picasa etc. But I am
ready to go that bit further and would like to start playing with layers,
erasing and pasting etc.
Adobe Photoshop CS3 is out of the question due to cost.
Does anyone have a view on Adobe Photoshop Elements 5, as against Corel
Paint Shop Pro XI?

I am not really in a position to say which one is better as I don't use any of them, but I will say that no matter which one you choose, stick with it.

Interface Lock-in
The interfaces of different raster- and vector-graphics editing applications are similar, but also just slightly different enough, that switching from one to another isn't always easy.

IMO the best thing you can do is to get trial versions of both applications and see what fits you best.

Does anyone have a view on Adobe Photoshop Elements 5, as against Corel
Paint Shop Pro XI?

Personally I would go with PS 5 or Corel. Never used Corel though, but I have used PS 5 and PS Pro and prefer PS 5 over the two.

I like photoshop, I refuse to use anything else... That is just personal preference though!