something more fast then that...openfile-refresh-save-close

Why have you included

Workbooks(Dir(Myfile)).RefreshAll

That seems unnecessary here

You should also stop all events and calculations before you start the loop and reset them after you the loop is completed

Your code modified

Sub aggiorna()
'With Foglio12
    Dim myWB        As Workbook
    Dim mySheet     As Worksheet
    Dim Myfile      As String
    Dim riga        As Integer
    Dim col         As Integer
    Dim num_righe   As Integer
    Dim xWS         As Worksheet
    Dim xComment    As Comment
    
    Set myWB = ThisWorkbook
    Set mySheet = myWB.ActiveSheet  '*  check if this the correct sheet
    num_righe = 500
    col = 7 'percorsi in colonna E
    riga = 5 'parte da riga 1

    With Application
        .EnableEvents = False
        .Calculation = xlCalculationManual
        .DisplayAlerts = False
        .ScreenUpdating = False
    End With
    
    For riga = 5 To 350 'num_righe
        Myfile = mySheet.Cells(riga, col).Value
        If Myfile <> "" And Dir(Myfile) <> "" Then
            Workbooks.Open Filename:=Myfile, UpdateLinks:=False
'            Workbooks(Dir(Myfile)).RefreshAll
            
            For Each xWS In Application.ActiveWorkbook.Sheets
                For Each xComment In xWS.Comments
                    xComment.Delete
                Next
            Next
            'Disable privacy settings warning
            Workbooks(Dir(Myfile)).Close SaveChanges:=True
        End If
    Next riga
    
    With Application
        .EnableEvents = True
        .Calculation = xlCalculationAutomatic
        .DisplayAlerts = True
        .ScreenUpdating = True
    End With
End Sub

Okay, clear, well, happy it speeded it up