Random classification of records

if you place the formula in a spare column and recalc the sheet, you should be close.
RANDBETWEEN( 1, 5 ),
you should then sum each assignment (1-5) to ensure you have a balanced distribution.

How can this be modified such that I have 4 equal-sized groups (n=40) and one group with n=41?

Without running a small macro, populating each cell, and keeping a running total, I don't know. The above will be close.
Do you have to repeat this, or is it a once-off?

I will need to repeat this.

A small macro does seem that it would be most helpful. I am unsure of the proper code to carry this out.

Might someone be comfortable putting this code together?

try this (you will need to add the vba-addin
In Excel, install the Analysis toolpack -VBA from Tools Addins.
Then in VBA, click Tools - References and put a checkmark on atpvbaen.xls
The problem with this is if you share your book, the other person must also have the analysis toolpack-vba addin installed.

Sub PopVals()
Dim vval As Long
Dim counts(5) As Long
x = 1
While x <= 201
  vval = WorksheetFunction.RandBetween(1, 5)
  Worksheets("Sheet2").Cells(x, 3) = vval
  vval = vval - 1
  If counts(vval) < 51 And vval < 5 Then
    counts(vval) = counts(vval + 1)
    x = x + 1
  End If
  If counts(vval) < 52 And vval = 5 Then
    counts(vval) = counts(vval + 1)
    x = x + 1
  End If
Wend

End Sub

The above isn't correct - please wait for a better response - I have to go.

Works perfectly. Many thanks!