To transpose or intelligent copy and paste?

Something like:

Sub foo()
Dim lCol As Long, lRows As Long
Application.ScreenUpdating = False
With ActiveSheet
    lRows = .Cells(Rows.Count, 1).End(xlUp).Row
    For lCol = 6 To .Cells(1, Columns.Count).End(xlToLeft).Column Step 5
        .Cells(1, lCol).Resize(lRows, 5).Copy .Cells(Rows.Count, 1).End(xlUp).Offset(1, 0)
        .Cells(1, lCol).Resize(lRows, 5).Clear
    Next lCol
End With
End Sub

This should do it, same idea:

Option Explicit

Sub TransposeDataGroups()
Dim LC As Long, Col As Long, NewSH As Worksheet

With ActiveSheet
    LC = Cells(1, .Columns.Count).End(xlToLeft).Column
    Set NewSH = Sheets.Add(after:=Sheets(.Index))
    For Col = 1 To LC Step 5
        .Columns(Col).SpecialCells(xlConstants).Resize(, 5).Copy NewSH.Range("A" & Rows.Count).End(xlUp).Offset(1)
    Next Col
End With

End Sub