A simple PIE prob

Question

In how many ways can we seat $5$ pairs of twins in a row of $10$ chairs such that nobody sits next to his or her twin ?
To count the number of possible arrangements with PIE it's simple to calculate the no. of ways in which we can seat $1$ pair of twins to be $9!.2.5$ but how to calculate the the ways in which we can seat more than $1$ pair of twins? For $2$ pair of twins it is ${5\choose{2}}.2^2.8!$ but it's getting messy for more pairs so is there any general way.