11 x 11 is the answer.. N=7 may result in larger square.
the Tangram I found w/ 5 rectangles are: 1x1,2x5,3x6,4x9,7x8 .
Good two Logophobic!
@buddy boy- thanks for the solution.. maybe I should have said " none of them have a common dimension" but I got a square rectangle piece.
@Dejmar- Yes its not like the Chinese Tangram in no. of pieces