Lazarus nemám, neviem aké funkcie pre porovnanie časov obsahuje...
V Delphi by som to urobil nejak takto:

unit Unit3;

interface

uses
  Winapi.Windows, Winapi.Messages, System.SysUtils, System.Variants, System.Classes, Vcl.Graphics,
  Vcl.Controls, Vcl.Forms, Vcl.Dialogs, Vcl.StdCtrls;

type
  TForm3 = class(TForm)
    Button1: TButton;
    procedure FormCreate(Sender: TObject);
    procedure Button1Click(Sender: TObject);
  private
    { Private declarations }
    Cas: TDateTime;  
  public
    { Public declarations }
  end;

var
  Form3: TForm3;

implementation

uses DateUtils;

{$R *.dfm}

procedure TForm3.FormCreate(Sender: TObject);
begin
  Cas := 0;
end;

procedure TForm3.Button1Click(Sender: TObject);
var T1: TDateTime;
begin
  T1 := now;
  if MinutesBetween(t1, cas) >= 5 then
   begin
     Cas := now;
     // Tvoj kod....
   end;
end;

end.