When a crack is detected in the heat exchanger of a furnace, particularly one that is relatively new (such as only five years old), the most appropriate action is to replace the heat exchanger under the manufacturer's warranty.
Heat exchangers are critical components of a furnace, responsible for transferring heat from the combustion process to the air that heats your space. A crack can lead to dangerous situations, including carbon monoxide leaks, which pose serious health and safety risks to the occupants of the building.
Taking advantage of the manufacturer's warranty not only ensures that you are following safety protocols but also helps maintain the integrity of the heating system. Warranties are designed to cover defects and issues that arise within a specified time frame, and using the warranty for a cracked heat exchanger is in line with proper maintenance and safety practices.
Using duct tape or other sealants might seem like a quick solution, but these methods do not address the underlying problem and can endanger safety. Running the furnace until it fails is not a safe practice and can result in further damage or hazardous conditions. Therefore, replacing the heat exchanger is the most responsible and effective course of action.