Will socket 775 heatsinks work with the new intel socket?

You mean 1156, or 1366? Depends on the cooler. If it's one like the Thermalrights that have different mounting brackets, yea, just get the right bracket for you mobo. Some don't have interchangable brackets though, and if it doesn't, than no.
 
If you're referring to the LGA1156 socket, it has different mounting hole spacing compared to LGA775, so you won't just be able to swap in an LGA775 cooler and have it fit. However, Thermalright should have an LGA1156 bracket available that will let you use your heatsink with the new socket.
 
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