Expected Value, Linearity & Advanced Probability · Challenge problem

Five cards are dealt from a standard $52$-card deck. The $13$ ranks are in the order $2,3,\ldots,10,J,Q,K,A$, with the ace counting only as high, so two ranks are adjacent if they are next to each other in this list ($K$ and $A$ are adjacent; $A$ and $2$ are not). What is the expected number of pairs of cards in the hand whose ranks are adjacent? Express your answer as a common fraction.