We reanalyze the strong lens modeling of the cluster of galaxies MS2137.3-2353 using a new UBVRIJK data set obtained with the ESO Very Large Telescope . We infer the photometric redshifts of the two main arc systems which are both found to be at z = 1.6 \pm 0.1 . After subtraction of the central cD star light in the previous F702/HST imaging we found only one object lying underneath . This object has the expected properties of the fifth image associated to the tangential arc . It lies at the right location , shows the right orientation and has the expected signal-to-noise ratio . We improve the previous lens modelings of the central dark matter distribution of the cluster , using two density profiles : an isothermal model with a core , and the NFW-like model with a cusp . Without the fifth image , the arc properties together with the shear map profile are equally well fit by the isothermal model and by a sub-class of generalized-NFW mass profiles having inner slope power index in the range 0.7 \leq \alpha \leq 1.2 . Adding new constrains on the center lens position provided by the fifth image favors isothermal profiles that better predict the fifth image properties . A detailed model including nearby cluster galaxy perturbations or the effect of the stellar mass distribution to the total mass inward does not change our conclusions but imposes the M / L _ { I } of the cD stellar component is below 10 at a 99 % confidence level . Using our new detailed strong+weak lensing model together with Chandra X-ray data and the cD stellar component we finally discuss intrinsic properties of the gravitational potential . Whereas X-ray and dark matter have a similar orientation and ellipticity at various radius , the cD stellar isophotes are twisted by 13 ^ { \circ } \pm 3 ^ { \circ } . The sub-arc-second azimuthal shift we observe between the radial arc position and the predictions of elliptical models correspond to what is expected from a mass distribution twist . This shift may result from a projection effect of the cD and the cluster halos , thus revealing the triaxiality of the mass components .