Nope.You can only crossfire cards of the exact same model,variant (like different ram or something) and manufacturer.
An example of Crossfire that can work is:
Sapphire Radeon HD 6950 2GB model paired with another card that's exactly the same
When you can't crossfire is in situations like this:
1 Sapphire Radeon HD 6950 2GB RAM paired up with a Asus Radeon HD 6990 4GB RAM because the cards are very different from each other in terms of how much ram they have (variants of each card),what manufacturer they are from and what card model it is
Here is where things may get a little confusing:
1.You have a Sapphire HD 6950 2GB RAm card and you also have a Sapphire HD 6950 1GB RAM yet they won't crossfire,but why?even though its from the same manufacturer and hte same model,the only different is the variation of RAM.Some people I know got caught out by this.
You can also crossfire in the following configurations:
crossfire (2 way)
3 way crossfire (Nvidia cards afaik don't seem to have a triple SLI,its just SLI or Quad SLI)
and finally Quad crossfire
I hope this post answers your questions on crossfire :-)
Pretty much absolutely nothing in this post is correct.
You can most certainly crossfire cards of a different type and brand.
Here is a link to AMD's crossfire guide:
http://sites.amd.com/us/game/technology/Pages/crossfirex.aspxHere is a link to the crossfire compatibility chart:
http://sites.amd.com/PublishingImages/Public/Graphic_Illustrations/WebBannerJPEG/AMD_CrossfireX_Chart_1618W.jpgI checked that guide myself as I wish to get another card at some point but not now (as PSU can't handle another card yet until suitable replacement is found).That chart only seemed to prove my point earlier about not being able to crossfire a HD 6950 (my current gpu) with say a HD6990 (the card I wish to add as an extra to my system). Yes I was wrong on my very 1st point (about same model and manufacturer) but It's a good thing that times have changed and compatitibilty is better now.My old card was a HD 4670 (which as we all know is utter crap for mining but good for most things I need to do,never had driver problems with it) and I based some of that info from other sites that were talking about the HD4xxx series cards.It's good that things are better now.I didn't know that from the HD5xxx series cards that compatibilty had improved until reading your post.
I guess it is true,you learn something new everyday.
I don't know if Im right on the modes of crossfire (2,tri-way,quad crossfire) but I do know that 2xHD6990 counts as Quad crossfire. (as each card has 2 gpus on it)
After seeing that guide,It's safe to say that I was right as the HD 5770 and HD 5830 can't be crossfired together at all (with or without the bridge connector) which should anwser the OPs question.