Well, you should now be aware of a few probelms with the transformer:
1) lots of leakage inductance, as you cannot interwind so many output turns to so few input turns. 2) Lots of capacitance to drive, as the inter-winding capacitance of the secondary is going to severely reflect back to the primary. After all, a 5KV secondary is going to have a *lot* of turns. Be careful with insulation, you will need some between the secondary and the coer itself. Have you picked a core and determined volts per turn for a "final" prototype?