Create a list of the sum of random numbers

I have a spreadsheet that contains a list of 5 random numbers (i.e. A1=RANDBETWEEN(1,10), A2=RANDBETWEEN(1,10), etc). At the bottom I have the sum of those random numbers (i.e. =SUM(A1:A5). This sum changes every time that I update the spreadsheet or hit "calculate." This is not the issue, as I want the random numbers to change.

My goal is to create a list of the sums of random numbers. (i.e. if the first set of random numbers were 1,1,1,1,1 then I would want to record the sum--5--in a cell. If, the next time I hit calculate, the set of random numbers became 2,2,2,2,2, then I want want to record the sum--10--in a cell directly below the previous sum--5--and have this continue every time the random numbers update/every time I hit calculate). Is this a possibility? Is it something that I would have to use VBA for?

Thanks.

You try this vba.

Private Sub WorkSheet_Calculate()
Application.EnableEvents = False
    Sheets("Sheet1").Range("A65536").End(xlUp).Select
    RowNum = ActiveCell.Row + 1
    Cells(RowNum, 1) = Worksheetfunction.sum(Range("A1:A5"))
    Application.EnableEvents = True
End sub