Real Challenge!! Sum every fifth cell in a column

I have an elaborate workbook with a summary page, I need to find a way to sum every fifth cell (sometimes sixth) in particular columns. Please see the attached screen shot for a better idea of what I am trying to accomplish. Obviously there is more data than you can see in the picture but it will give you the idea of the pattern used. The sum of these cells will go at the bottom of the column and must have the ability to move down when more data is added. Would I be able to use a dynamic named range to do this, will it have to be VBA, or is it not possible? I can't change the layout of the data due to the other sheets in the workbook. It also needs to automatically update if another course is added (grouping of five rows). Please help, I have countless hours in this product and this is all that is stoping it from being perfect.