Set the form's TimerInterval property in the Click event of that command
button.

Add a declaration for a Static variable in the Timer event to keep track of
how many times the code's been executed, and set the TimerInterval to 0 once
you've hit the desired limit.

Private Sub Form_Timer()

Static intIterations As Integer

 Me!lblBlink.Visible = Not Me!lblBlink.Visible
 intIterations = intIterations + 1

 If intIterations >= 5 Then
   Me.TimerInterval = 0
   intIterations = 0
 End If

End Sub

(Of course, I'd caution against putting flashing on your form. It can
actually cause medical problems for certain users!)

You won't need the Timer. In the command button code (air code):

Sub MyButton_Click()
Dim i As Integer
For i = 1 To 10 ' 5 on, 5 off
   Wait (0.5) ' 1/2 second
   Me!lblBlink.Visible = Not Me!lblBlink.Visible
Next i
End Sub

Public Function Wait(sngSecs As Single)
' Timer is a keyword that retrieves the number of seconds
' since midnight as a single
Dim sngWait As Single

sngWait = Timer + sngSecs
While Timer < sngWait
   DoEvents
Wend

End Function