We have 5 "people" to arrange:

.$\displaystyle \boxed{Aa}\;\boxed{Bb}\;\boxed{Cc}\;\boxed{Dd}\;\b oxed{Ee}$

There are:

.$\displaystyle 5! \,=\,120$ permutations.

But for each permutation, the couples can be "swtiched".

. . $\displaystyle \boxed{Aa}$ could be $\displaystyle \boxed{aA}$, $\displaystyle \boxed{Bb}$ could be $\displaystyle \boxed{bB}$, and so on.

There are:

.$\displaystyle 2^5 \,=\,32$ possible switchings.

Therefore, there are:

.$\displaystyle 120\cdot32 \:=\:{\color{blue}3840}$ seating arrangements.