The Ising models in five to seven dimensions are simulated on the Creutz cellular automaton with the three- to five-bit demons on finite-size lattices. The simulations result in overlapping curves for both the order parameter and the internal energy. However, the magnetic susceptibility and the specific heat curves converge to the limiting ones as the number of bits increases. By fitting the order parameter data within the temperature interval where the infinite lattice is approximated, to a power law with correction and by using the renormalization group prediction for its leading critical exponent as the criterion, the value of the critical temperature for the infinite lattice is obtained. For the Ising models in five to seven dimensions, they are in agreement with the Monte Carlo and the series expansion results.