oh dear, it's one of those with a little light in it. Might even be 12volt. Is it directly above the bath or shower?
I will guess that it is about 4" across and has a flexible convoluted hose on it, probably draped across the ceiling and hopefully exiting through a vent in the wall or soffit. There is a good chance the hose will have water lying in it from condensation. If you are unlucky it might just vent into the loft, causing damp and rot.
Does it come on with the light switch? Does it have a timed run-on after you turn the light on?
A very much better fan is one of this inline ducted fans, that can go in the loft.
160m3/hr 31dB(A) is usually sufficient]]
but as you have quite a bad damp problem you might prefer to go to this extra-powerful 350cu.m 33dB(A) but you would need to increase the duct size, to 125mm (5 inches)
There are some cheaper brands which may not be as good.
It is always preferable to use rigid ducting rather than flexible, as it is less retentive of fluff and condensation, and can be angled slightly so that any water runs out. At the very least the ducting should be wrapped in loft insulation to prevent it being so cold that it encourages condensation.
For comparison, I think your old fan is probably one of 41dB(A) these weedy little things or similar which builders choose because they are cheap rubbish and are noiser than the ones I suggest.