Help with code efficiency - routine takes WAY too long to run

I'm a VBA novice. I have a spreadsheet with 5 columns of data in columns A through E with any number of rows (usually thousands). The problem is that for some of the rows the data is shifted to the right one column (in columns B through F). I wrote a macro to shift the rows that were off; the macro evaluates each row and if column A is empty, it cuts the 5 cells to the right and pastes them and then moves to the next row, if not empty it just moves to next row. What I came up with works, but takes way too long and heats up my laptop. I've searched ways to make the code more efficient, but have not come up with something that does the trick.

I'm requesting two things. First, given the code I have (the process of checking each row one by one), is there something I can do to make it run faster? Even if there is a better way to approach this, I'd love to learn how to make something like this faster if that is possible.

Second, I know there has to be a better way to approach this. Any suggestions will help me learn how to do things better.

Thanks in advance.
Doug

Sub Shift()

Application.ScreenUpdating = False
Dim RowCount As Integer
Dim lRow As Long
    
'Finds the last non-blank cell on a sheet/range.
    lRow = Cells.Find(What:="*", _
                    After:=Range("A1"), _
                    LookAt:=xlPart, _
                    LookIn:=xlFormulas, _
                    SearchOrder:=xlByRows, _
                    SearchDirection:=xlPrevious, _
                    MatchCase:=False).Row

' move cursor to cell A1    
    Range("A1").Select
    ActiveCell.Offset(1, 0).Select

For RowCount = 2 To lRow

    If ActiveCell.Value = "" Then
       ActiveCell.Offset(, 1).Resize(1, 5).Cut
       ActiveSheet.Paste
       ActiveCell.Offset(1, 0).Select
    Else
       ActiveCell.Offset(1, 0).Select
    End If

Next RowCount

Application.ScreenUpdating = True
End Sub