We present a numerical method for inverting long-period components of lightcurves of asynchronous binary asteroids. Data of five near-Earth binary asteroids, (175706) 1996 FG 3, (65803) Didymos, (66391) 1999 KW 4, (185851) 2000 DP 107 and (66063) 1998 RO 1, for two of them from more than one apparition, were inverted. Their mutual orbits' poles and Keplerian elements, size ratios, and ellipsoidal shape axial ratios were estimated via this inversion. The pole solutions and size ratios for 1999 KW 4 and 2000 DP 107 are in a good agreement with independent estimates from radar measurements. We show that uncertainties of estimates of bulk densities of binary systems can be large, especially when observed on short arcs.