Hi Ken,
Welcome to the board.
OK, if you were doing this manually a simple copy and paste would have the same effect, right? It'd copy the border too. So, you'd actually do a copy and then PasteSpecial and choose values only. Voila, no borders.
To get the syntax for doing this (and for many other areas where you may need a quick reminder) just use the good old Macro Recorder and then examine the code. A little editing of the recorded code gives us:
Sub Macro1()
Worksheets("Sheet1").Range("B4").Copy
Worksheets("Sheet2").Range("E5").PasteSpecial _
Paste:=xlPasteValues, Operation:=xlNone, SkipBlanks:=False, Transpose:=False
End Sub
HTH