Dim Connection As ADODB.Connection
Dim AdoCommand As ADODB.Command
Dim RS1 As ADODB.Recordset
Set Connection = New ADODB.Connection
   
Dim BeginRow As Integer
Dim BeginColumn As Integer
Dim FirstCell As String

Dim xlWorkBook As Workbook
Dim xlSheet As Worksheet

Set xlWorkBook = ThisWorkbook
Set xlSheet = xlWorkBook.Worksheets("Лист1")


Connection.ConnectionString = ....
Connection.Open

Set AdoCommand = New ADODB.Command
    AdoCommand.CommandTimeout =  120 

Set AdoCommand.ActiveConnection = Connection
    AdoCommand.CommandType = adCmdStoredProc
    AdoCommand.CommandText = "dbo._myProc"

    
    Set RS1 = AdoCommand.Execute

     xlSheet.Range("A5").CopyFromRecordset RS1 ' работает

     xlSheet.Range(xlsheet.Cells( 5 ,  1 )).CopyFromRecordset RS1 ' выдает ошибку: Method 'Range' of object '_WorkSheet' failed 

   ' Однако такая конструкция проходит на ура:
     xlSheet.Range(xlSheet.Cells( 5 ,  1 ), xlSheet.Cells( 15 ,  67 )).Value = "ku-ku"
   

End Sub

Dim rng As Range
Set rng = xlSheet.Cells( 5 ,  1 )
rng.CopyFromRecordset RS1