Ok, let’s analyze your Lasair III particle counter printout - we use the same one. Your have two resulting colomns - Delta and Summ. For example for 0,5 microns raw you have Delta = 3492 particles/m^3 and Summ 6215 particles/m^3. It means, that particle counter has determined 6215 particles/m^3 of size >= 0,5 microns, and actually in range 5,0 - 1,0 - 3492 of the total amount. It easy to check: 6216 - 3492 = 2723 particles/m^3. It directly corresponds to the value, shown in next raw and applicable for particles >= 1,0 micron.
So first your value to compare with ISO 8573-1 requiremnets it’s definitely Delta between 0,5 and 1,0 - first raw and first resulting colomn. This value is 3492 particles/m^3 and your result is ok (it less then 90 000 and even enough for Class 2 <=6000 particles/m^3).
Then another range. A little bit more complicated, but also not too much. The required range is between 1,0 and 5,0 microns. And particle counter suggest more detailed info - Delta between 1,0 - 2,0 microns and between 2,0 - 5,0 microns - you need simply to add them - in your case it will result in 1350 +1097 = 2 447 (in this case it is not enogh for Class 3 and only corresponds to Class 4 < = 10 000 particles/m^3).
Actually it’s too much for this range - do you utilize high pressue diffusor: http://www.prager-elektronik.at/datenblaetter/PMS/HPDIII.pdf
What the system is that - which compressor, which filters, which distribution system? Was is treated after construction - cleaning, passivation? Which the intended use - instrumentation air for valves or for sterilizing filtration of aseptic products?