Because the primary consists of two coils, that are switched on alternately, you treat it as having 5 primary turns.
However.
It isn't quite as simple as Ns/Np * Vin. The primary voltage will be much larger than Vin, and so the output voltage will be higher. If there are built-in diodes in the transformer (as many tv/crt flybacks have) then for half the switching cycle, energy will be stored in the core. It is also somewhat dependent on switching frequency and the characteristics of the transformer. For the most part you simply treat the output as 'being high voltage'. It would be very difficult to calculate the actual voltage with any sort of precision, as it is also dependent of spark gap length.
The fact you're asking this is worrying as you could well be dealing with lethal high voltage without know the basics of how the circuit works. I understand wanting to make cool sparks (I too have built lots of high voltage stuff) but there are plenty of things that can go wrong, which, at best, will mean the circuit simply doesn't work/oscillate. At worst, you blow up components.