It looks like you could copy|Paste the visible cells in the autofilter range,
then come back to copy|paste the 5th column over the 3rd column.

If that's something you want to try:

Option Explicit
Sub testme()

   Dim myRng As Range
   Dim DestCell As Range
   
   With Worksheets("sheet2")
       'next open cell in column A???
       Set DestCell = .Cells(.Rows.Count, "A").End(xlUp).Offset(1, 0)
   End With
   
   With Worksheets("sheet1")
       With .AutoFilter.Range
           If .Columns(1).Cells.SpecialCells(xlCellTypeVisible) _
                  .Cells.Count = 1 Then
               MsgBox "nothing visible in the filter!"
               Exit Sub
           End If
           Set myRng = .Resize(.Rows.Count - 1, .Columns.Count) _
                           .Offset(1, 0).Cells.SpecialCells(xlCellTypeVisible)
           myRng.Copy _
               Destination:=DestCell
           
           myRng.Columns(5).Copy _
               Destination:=DestCell.Offset(0, 2)
       End With
   End With
       
End Sub

I didn't know where to paste, so I just used the next available cell in column
A.