Use two stage power conversion for your application (AC to DC front end converter for 420Vac to 800 VDC conversion. A ZVS phase shifted interleaved fullbridge for 800VDC to 5KVDC)
Try VIENNA rectifier for front end converter purpose.https://en.wikipedia.org/wiki/Vienna_rectifier
Use multiple outputs in fullbridge (8 outputs, each output voltage is 625V). After rectification add all these outputs in series connection to get 5KV.
i hope your are expert in power electronics design, because it is very tough requirement. I suggest to you initially make a scale down (1.2KW) prototype.