Threshold law for the process e + A q + --. A (q + 4) + + 5 e has been derived within the classical theory. For neutral targets (q = 0) the threshold exponent assumes value 5.08, consistent with previous calculations for ionizations of lower orders. The method fails for q < -4. The results are compared with recent experimental measurements, which considerably underestimate theoretical findings. An empirical formula for n-fold ionization is provided, which predicts values for the threshold exponent ~c= 7.8 and 12.5 for n = 5, 6 respectively.