In trapezoid $KLMN$, $KL$ and $NM$ are perpendicular to $\overline{KN}$. The sum of the lengths of the parallel sides, $KL$ and $NM$, is equal to the length of the non-parallel side $LM$. Given $KL=5$ and $NM=12.8$, what is the length of $\overline{KN}$?