There isn't really any history between Cormier and Silva.
Cormier was a heavyweight title contender until a couple years ago. He only dropped to LHW because he didn't want to fight his friend and training partner, Cain Velasquez, for the title. DC was an Olympic wrestler. Silva is one of the greatest fighters in history. His striking, and cockiness in the ring, was second to none.
On paper, this is a striker vs wrestler matchup that should favor Cormier because he's built bigger and has taken hard shots from heavier opponents for years. Silva does have a chance though, because his striking is so elite. His chin has faded some though over the years. I expect a dominant DC victory, but you never know.