Would that be fast enough for the OP's 500Hz requirement?
Anyway, the problem with reed switches isn't the switch gap, which is in vacuum and typically can handle very high voltages, but with the insulation between the reed's leads and the low-voltage magnetic coil. I've used may HV reed switches made with special potting compounds, only to have them eventually fail with a carbon breakdown path forming inside the potting material between one lead and the coil.
10kV insulation is a considerable challenge over say 5kV.