Is it permissible to prepare food on behalf of a deceased father five months after his death and offer it to people without specifying a time?

It is not from the Sunnah for the family of the deceased to prepare food and invite people to it, because the Prophet (peace and blessings be upon him) and his Companions did not do so. Food can be prepared and given as charity on behalf of the deceased, provided that it is not accompanied by a gathering.