Hmm but the guy from the Poland embassy told us that if we obtain the Poland National Visa, we cannot visit other parts of Europe, eg Germany for more than 5 days.
It's nonsense - the old regulations said that, but as you're from Singapore - you don't need to worry about the 5 days anyway, because you have the right to 90 days in 180 in Schengen anyway.
So will they consider my days in Poland as part of the 90 days too if I have a Poland National visa?
No - it's only counted from when you use it. It's advised to keep with you a record of all your trips, so you can prove how long you've spent in non-Poland Schengen - in your case, you'd be back to 90 days with the trip. Essentially, one day in the zone must be equalled with one day out of the zone (or in a country for which you have a national visa). In your case - you'll have 60 days left, but then as you spend 65 days 'out of zone' - you'll be back to 90 days.
The embassy is quite frankly wrong - en.wikipedia.org/wiki/Schengen_Area#Schengen_visa