No part of any parking area for more than five (5) vehicles shall be closer than twenty feet to any dwelling unit, school, hospital, or other institution for human care located on an abutting or adjoining lot, unless separated by a solid wood privacy fence or other approved constructed screen of between four (4) and six (6) feet in height. If on the same lot with a one-family residence, the parking area shall not be located within the front yard required for such building. In no case shall any part of a parking area be closer than four feet to any established street or alley right of way.