To design a 5-bit comparator using a single 7485 and one additional gate, you can utilize the 7485's built-in capabilities to compare two 4-bit numbers. Connect the 5th bit as an extra input; for instance, use a logic gate (e.g., AND gate) to determine the relationship of the 5th bits of the two numbers. The output of the 7485 can indicate if the first number is greater than, less than, or equal to the second for the first four bits, while the gate can adjust the result based on the 5th bit comparison. This way, you effectively extend the functionality of the 7485 to handle a 5-bit comparison.