you haven't provided enough information
If you want a pulse transformer that can be directly driven from a Ka3525 that may turn out to be a difficult task if you want to go as low as 5Khz.
You may have to use an expensive amorphous metal core, rather than a standard ferrite transformer to do that.
most people just use an amplifier, two transistors, or two mosfets to drive the pulse transformer.
also, did you put a capacitor in series with the primary winding? if not then the transformer probably got saturated.
when calculating the number of turns you must use the lowest frequency.
on the surface it sounds like you have enough turns.
what is the core area of your transformer, flux density, permeability, air gap, ?