Since each member must sit next to two members of the other party, the seating arrangement must be alternating between Democrat and Republican.

We have \(5!\) ways to seat the Democrats and \(5!\) ways to seat the Republicans. However, since we can rotate the seatings to match each other, we have to divide by \(5\).

Therefore, there are \(5!5!/4=2880\) different seating arrangements.