In a thread here someone thought that a 1725 motor probably has the same
mechanical structure as a 3450 & hence could be run at 120 Hz. My
question is: if a 1725 motor is mechanically the same as a 3450 motor, do
you think that it could be run at 5175 rpm?

The only way to know is to test to destruction.

As a data point, I have several days of run time on a 7.5 hp 1725 at
4000rpm.

Karl