what methods could I use to step-up 700VDC to 5000VDC(approx)?
A switching regulator is the best way to go about this. You take your 500VDC input, chop it at high frequency, apply the chopped signal to a magnetic component (inductor or transformer) to create your higher voltage, then re-rectify it to get DC out.

If you don't care about isolation between input and output, you can use a boost converter.

If you need isolation, as Olin said you can use a flyback converter, which uses a transformer to achieve galvanic isolation between input and output.

It's difficult to get from 5-15V to 5kV with a single-stage converter (the duty cycle would be a challenge) so your intermediate stage of 700V isn't actually a bad idea. You lose a bit on efficiency with cascaded converters, but at least the conversion is feasible.