Custody of the child is based upon the best interest of the child. Bigamy does not relate to the child. So no it would not help in a custody case....

Being that I have had no contact in 5 years, is there any easy way out to make sure I am no longer legally married?

You need to call the clerk of court for the county where you were married, or where she was living and see if she filed for divorce. If not then...