Can a Corsair CX430 handle a Radeon 5830?

Well, if you already have the GPU, give it a shot. Worst that could happen is that either the compy doesn't boot with it in, or it shuts down when playing Crysis with it in.

It looks like the card itself needs up to 170W. Browse through some reviews:
http://www.techpowerup.com/reviewdb/Graphics-Cards/ATI/...

Guru3d review suggests that you need 35-40A on 12V rail and xbitlabs measured 467W of power draw (linpack + furmark), but both reviews use heavily overclocked lga1366 i7s.

All in all, I think it all depends on a cpu you are going to use and its OC level.
I guess you don't plan > 4GHz overclock, and those 170W is a extreme situation (furmark etc), so for normal usage even with some gaming I think this PSU is enough.

Though I wouldn't advise you to take my advice. Always get a second opinion.

Games are not going to be played on this PC though. The 5830 I have is HDCP complaint where the 550Ti isn't, and for BD-R movies and HD streaming content that's an absolute must.

I was just thinking of something heavily taxing for the card, and Crysis came to mind.

But the same principle applies. Try playing a few HD movies and see how it goes.

Aside from the power though I'm also wondering how that's all going to fit into the case. The Radeon 5830 is a 10.5" card and Silverstone says the case is rated for cards up to 12". I'm wondering how tight of a fit it's going to be.