I'm surprised at the mechanic's recommendation of not leaning below 5,000 feet. The 5,000-foot rule is designed to protect an engine. If the mixture is leaned and the pilot calls for full power-at altitudes where the engine can achieve high power - there can be damage to the engine. At 5,000 feet, most normally aspirated piston engines can't produce more than about 75 percent of power, so manhandling the throttle won't cause a problem. But there's no reason not to lean an engine at altitudes lower than 5,000 feet as long as it's enriched before the throttle is advanced to call for full power, as in a go-around. If you do find yourself running low on fuel, it's important to alert the controller to your problem. You have two options. You can advise that you are "minimum fuel," or you can declare an emergency. If you declare "minimum fuel," air traffic control has no obligation to give you priority handling. "Minimum fuel" means that your fuel supply has dwindled to a level where you can't accept any undue delays. If you need priority handling, declare an emergency and let the controller know how many minutes of fuel you think you have remaining. The paperwork for declaring an emergency is nothing compared to that required if you run out of fuel.