Use a TFR (non caustic)....it wil need diluting,alternatives are available although they all really do the same thing to the grime.Gardiners do one called ecover i think,and i know a few of the guys like this one...sorry i haven't got a link.
When applying it at that height you will have to use an old brush and dip it into the solution and then scrub the gutters/fascias,but just make sure that if you do get any on the glass DONT let it dry because it is a sod to get off,especially at height because you cant really see the ghosting effect of the chemicals.