Read the airport destination before boarding
Terminal 4 is not merely the stop before Terminal 5. The two terminals sit on different Piccadilly line branches, so a train displaying Heathrow Terminal 5 will not call at Terminal 4. Check the front of the train and the platform display before boarding, especially at a busy central station where several westbound destinations share the same platform. If you board the wrong Heathrow train, the clean correction is usually at Hatton Cross; waiting for the right branch is quicker than reaching the wrong terminal and trying to cross the airport with luggage.