Overload Class

There might be nuisance trips, but otherwise acceptable. If it runs only 5 seconds, it is not clear that an overload is even meaningful at that speed.

2 completely independant windings?

What does the rating plate mention for each speed?

I suppose the motor is designed to run at a given power at 100 % ED at speed 1 and another given power at 100 % ED at speed 2.

The overload class implies the LRA withstand as i understand it. If the motor does not start at all, it should still be able to withstand 7.2x FLA for 10 secs...shouldn't it ? As most motors are designed to withstand DOL starting, this should not be a problem even in your case. i don't think you need a special Class 5 relay. But then, i have no experience with pole-changing motors, so please excuse my ignorance,

I'm with Tornado on this. The purpose of an overload relay is to provide protection against a condition that might damage the motor, not to provide tripping at as low a level as possible. So what if your motor never trips with a class 10 overload? Why is that a problem for you? The motor is likely designed for Class 10 protection or better, that's all you need for it, regardless of how long it is used.

Pipe down and be happy!