A person who is inadmissible to the United States would be precluded immigration through EB-5. The law on inadmissibility due to a criminal conviction is located at INA 212()a)(23). One would have to look at the specific language of the statute which you had violated to provide a definitive opinion. However, in most states of the United States common assault does not involve the requisite mental intent to become a crime involving moral turpitude and does not rise to the level of a serious crime. Thus, common assault would not make you inadmissible. However, domestic violence could cause you problems. I suggest that you have an attorney consider the specific language of the convicting statute before investing considerable sums. Nevertheless, a caution may not even be a crime. In that case, your caution would have no impact on immigrating through an EB5 investment.