To determine the correct set of statements that describe the steady state speed-torque characteristics of a three-phase synchronous motor, let's analyze each statement given in the options:

1. Runs at constant synchronous speed: This statement is true for synchronous motors because they are designed to operate at a constant speed, which is the synchronous speed. The synchronous speed is determined by the supply frequency and the number of poles of the motor.
2. Starting torque is zero: This statement is also true. Synchronous motors do not produce any torque at standstill as they require an external means to reach near-synchronous speed before they can lock into sync with the supply frequency.
3. Torque increases significantly with slip: This statement is false for synchronous motors. Unlike induction motors, a synchronous motor does not have slip under normal operating conditions. The torque of a synchronous motor does not increase with slip because it operates at synchronous speed.
4. Not suitable for variable speed drives: This statement is conditionally true, but it depends on the context and technology used. Traditionally, synchronous motors are not preferred for variable speed applications without additional speed control mechanisms.
5. Maintains speed under varying loads: This statement is true. A key feature of synchronous motors is their ability to maintain a constant speed regardless of load variations, as long as the load is within the motor’s capacity and the power supply frequency remains unchanged.

Based on the analysis, the correct set of statements is:

• (i), (ii), and (v) only

This answer correctly describes the characteristics of a three-phase synchronous motor as it operates under normal conditions.