こういうことでは?
Private Sub Worksheet_Change(ByVal Target As Range)
Dim myRange As Range, r As Range
Set myRange = Intersect(Target, Range("A1,E1").EntireColumn)
If myRange Is Nothing Then Exit Sub
Application.EnableEvents = False
For Each r In myRange
If r.Value <> "" Then
Select Case r.Column
Case 1
Cells(r.Row, "D").Value = Date
Case 5
Cells(r.Row, "F").Value = Date
End Select
End If
Next
Application.EnableEvents = True
End Sub