Honestly what you want to do is a waste of money.
1. The 5770 only supports 2 way Crossfirehttp://www.amd.com/en-us/products/graphics/desktop/5000/5770
2. For the cost required parts you could get a new gpu that would be faster than those 4 old cards even if you somehow manage to force 4 way crossfire. Plus aterblocks will probably be difficult to impossible to find as they are usually only made for the high end cards the 5770 was an entry level gaming card. Even if they were made they were likely discontinued long ago.