As far as a VBA solutions is concerned, below is a worksheet event.
It will not message the user before you paste what is in your Excel clipboard but will do so if you're about to select multiple rows/columns/cells. From a user experience standpoint, this is likely good enough.
Private Sub Worksheet_SelectionChange(ByVal Target As Range)
If Application.CutCopyMode <> False And Target.Cells.Count > 5000 Then
MsgBox "Excel is in cut/copy mode..."
End If
End Sub
This would need to go into each worksheet you want the warning to occur.
EDIT: OR! Use the below in ThisWorkBook
Private Sub Workbook_SheetSelectionChange(ByVal Sh As Object, ByVal Target As Range)
If Application.CutCopyMode <> False And Target.Cells.Count > 5000 Then
MsgBox "Excel is in cut/copy mode..."
End If
End Sub
EDIT2: The above only works on the active workbook. For using it in a personal workbook, Pearson did a good job of explaining how something like this could work for all workbooks (even non macro files), here.
The big change I expect is when they explain the below. I can't test it right now, but I expect Workbook_SheetSelectionChange(...) to be the thing to make it work.
Private XLApp As CExcelEvents
Private Sub Workbook_Open()
Set XLApp = New CExcelEvents
End Sub