VBA code to copy, paste and transpose every 5th row from multiple worksheets

There is no "Statatest" sheet on your example workbook. Make a sheet called Statatest, copy columns AB from "Sheet6" (so it looks nice) and run this code. It matches what you had on sheet 6.

Sub Copy_Data()
Dim fWS As Worksheet:   Set fWS = Sheets("Statatest")
Dim ws1 As Worksheet:   Set ws1 = Sheets("Productivity")
Dim ws As Worksheet
Dim iCol As Long, LC As Long, LR As Long, aCount As Long

Application.ScreenUpdating = False

For Each ws In Worksheets
    Select Case ws.Name
        Case Is = fWS.Name
            'do nothing
        Case Is = ws1.Name
            aCount = 3
            ws1.Range("B6:B" & ws1.Range("B" & Rows.Count).End(xlUp).Row).Copy
            fWS.Range("C1").PasteSpecial xlPasteAll, Transpose:=True
                LC = ws1.Cells(10, Columns.Count).End(xlToLeft).Column
                If LC > 1 Then
                    For iCol = 3 To LC
                        LR = ws1.Cells(Rows.Count, iCol).End(xlUp).Row
                        ws1.Range(ws1.Cells(10, iCol), ws1.Cells(LR, iCol)).Copy
                            fWS.Range("C" & aCount).PasteSpecial xlPasteAll, Transpose:=True 'every 3rd row
                        aCount = aCount + 3
                    Next iCol
                End If
        Case Is = "Terms of Trade"
            aCount = 4
            LC = ws.Cells(10, Columns.Count).End(xlToLeft).Column
            If LC > 1 Then
                For iCol = 2 To LC
                    LR = ws.Cells(Rows.Count, iCol).End(xlUp).Row
                    ws.Range(ws.Cells(10, iCol), ws.Cells(LR, iCol)).Copy
                        fWS.Range("C" & aCount).PasteSpecial xlPasteAll, Transpose:=True 'every 3rd row
                    aCount = aCount + 3
                Next iCol
            End If
        Case Is = "Gross Government Debt"
            aCount = 2
            LC = ws.Cells(10, Columns.Count).End(xlToLeft).Column
            If LC > 1 Then
                For iCol = 2 To LC
                    LR = ws.Cells(Rows.Count, iCol).End(xlUp).Row
                    ws.Range(ws.Cells(10, iCol), ws.Cells(LR, iCol)).Copy
                        fWS.Range("C" & aCount).PasteSpecial xlPasteAll, Transpose:=True 'every 3rd row
                    aCount = aCount + 3
                Next iCol
            End If
    End Select
Next ws
    
Application.ScreenUpdating = True

End Sub