We present a detailed investigation of the twin microstructure of 5M Ni-Mn-Ga single crystals with very low twinning stress. We show that the twin microstructure is komplex one and that approximation of the 5M crystal structure by a tetragonal lattice does not suffice to explain all observed features, while monoclinic approximation with modulation taken in account seems to describe most features. The monoclinicity and modulation of the lattice actually seems to be tightly associated with the extraordinary low twinning stress of the studied alloys.