In practice, when dealing with reactive loads (motors are inductive), it’s best to use higher power handling parts. Notice that the rating on the relay is for “resistive load”. A motor is an inductive load, not a resistive load. A simple resistive load simply dissipates energy into heat at a steady rate. An inductive load STORES energy in a magnetic field. In a motor, this stored magnetism in a stator winding (inductor) is then opposed by the opposite field polarity of the rotor winding – the magnetic energy is now “spent” as kinetic energy, spinning the rotor until the two electromagnets are in phase. So, an inductor stores and releases energy as magnetic reluctance. A resistor simply releases energy.
All of this happens over time. The Henry, which is the SI unit of inductance, is defined as 1 henry = 1 ampere of change per second producing 1 volt. The key is the change / ampere per second thing. Time. The electrical characteristics of an inductor are highly dependent upon time. Simple example is, our 60 cycle AC power applies x amperes in 1/60th of a second and results in an AC motor turning at the equivalent rate.
The problem comes when you electrically disconnect an inductor. If you suddenly disconnect an inductive load, like a motor, the electrical current is almost instantaneously removed, but the stored magnetic field is not. In your 25 amp 5HP motor, 25 amperes charging the inductor at 1/60th of a second now becomes something like 25 amperes in 1/100,000 second. The power stored in the inductor is now sort of “whip-lashed” into dissipating very rapidly. The rotor can’t absorb it, because it can’t do a sudden full turn in 1/100,000 of a second. So, pressure builds up in the inductor. In electricity pressure = voltage (electromotive force).
The pressure keeps building and building faster than the motor can handle, and can become millions of volts over a matter of milliseconds. This can be a problem in a lot of different ways, but in this case: the voltage generated is high enough to arc across the relay contacts which are disconnecting and dump all of the energy in 1uS to reach ground. If the relay is a solid state relay (mosfets or igbts), it’s a pretty spectacular explosion of blue smoke and shrapnel. In this case, though, the relay is mechanical, so there is an arc of electricity jumping across a gap of air or gas. Put simply, this is an arc welder. Bang, your relay is now welded together.
TL;DR – Suddenly disconnecting an inductive load causes an instantaneous release of energy from the collapsing magnetic field. This could arc weld the relay contacts together as the energy dissipates to ground. In reality, the pressure switch mechanism and a snubber circuit dissipate this energy somewhat, but the very brief power across the relay is HIGH, and will exceed the steady state power. So, get a relay that is rated higher. It will also have larger contacts that conduct this instantaneous current rather than heating and melting.
P.S. Any physics nerds feel free to correct any oversimplifications or errors I may have made in explaining this.