Worksheet Change Event-what I expect it to do

I have the following code:

Sub TabName()
    ActiveSheet.Name = ActiveSheet.Range("A5")
End Sub

The above code works fine, though I have to run the macro each time manually.

I am trying to make it dynamic using the following code:

Private Sub Worksheet_Change(ByVal Target As Range)

   If Target.Address = "$A$5" Then

        ActiveSheet.Name = ActiveSheet.Range("A5")

   End If

End Sub

This code does not do what I expect it to do, which is rename the sheet if i change the text in cell A5.

Any help would be appreciated.