I would try uninstalling the font, clearing the Adobe font caches, and reinstalling the font.

One thing is not clear to me: Once you speak about spaces, then you speak about en/em dashes. Spaces (blank) or dashes (horzontal bars)?

Oh, sorry! Sloppy of me, what I mean is still SPACES. I have used a lot of indents, Em space in this case, that is appearing very narrow. Thanks for pointing that out. Also the width of the normal space seems a bit off too, but I know where to edit this, and it shouldn't be affected by the same settings as the en/em space right?

I have tried to export new versions of the font without any luck. In fact, I have two fonts deriving from the same Fontlab project, and they both have this issue. It's just strange that it worked fine in CS3. Unfortunately I removed CS3 before noticing this problem, otherwise I could have just finished it there... But now I am curious to understand why this is happening and how to fix it. There must be some settings controlling these measurements? Or is it defined by InDesign? An Em space for example is always as big, no matter which typeface you use right? A square in the same point size as you are currently using?

Problem solved! Thanks for that K.L.
The font had glyphs for en/em space amongst others that CS3 apparently didn't read, but CS5 did. I simply deleted all redundant glyphs and then it worked fine.

Were you creating indents by inserting spaces? You'll have greater control and flexibility if you use Paragraph settings, or even better, Paragraph Styles to handle that sort of thing.