Not that great of an idea. First, that PSU is absolutely horrible. You really can't get much lower quality. You really shouldn't trust it at all. Instead, grab the Rosewill Challenger case for $55 and pick up a good Antec 430W for $45. You'll end up spending more, but it's worth it.
Second, you're wasting a good $15 on a DVD burner. The cheapest ones are usually around $16 with no shipping, and there is no difference between models.
Finally, while the HD 5670 is decent, I don't consider it good for gaming. I'd HIGHLY recommend trying to fit the HD 5770 in the build for $30-40 more. You'll get a huge amount of additional power for not much added cost.
I fail to see how "every one of them" causes the price to go over $400 when two of the four are CHEAPER than what you've picked out. The DVD burner saves $14, the RAM saves $6. Of course, that's counting shipping, which you didn't consider in the original post. With all the parts you've choosen, the total shippng is $22, which makes the total cost would have been $417 after rebates, which is already over the $400. If you just change the RAM, optical, case/ and PSU, you'd spend the exact same. If you didn't change the case, you'd actually be under budget by $3. I know the 5770 will put it over $400, but it's well worth the $41 you'd be over budget, counting the $14 you're already over for shipping.
By the way, that optical drive you linked to isn't $23. It's $26, with $4 shipping.
^That's a good deal, but the Antec 300 isn't as good of a case as the Rosewill Challenger. It only comes with a single fan. Also, the BP430 is lower quality than the Earthwatts 430W. Still, using that deal, the HD 5770 then comes into budget. Actually, with all the changes I've suggested, and that combo, the total comes to $401 with shipping.
Forgot about that top fan. I never count the number of spots where you could add fans. Given how much fans cost, you'd do better just to buy a case with the number of fans needed than to buy a cheaper one without the fans. Here's the direct link to the case on Newegg.
I'd wait on the DVD burner. There is typically one on Newegg for $16 or $17 with free shipping. No reason to pay even an extra $3 on a non-essential, non-performance part.