Almost any coax can be rated for 5kV with >= 1mm of dielectric insulation but only the ones with this specification will likely be guaranteed because voids in the plastic or contaminants may cause partial discharge (PD) impulses when exposed to this kV DC level. You can choose a coax suited to the rise time of pulses you desire (BW=0.35/Tr) and the impedance of your instruments (50 or 75) and thus the connectors for same. There are substantial differences if you wants xx picosecond rise time vs xx nanosecond. Each electron PD discharge will cause some degradation of the electrode by accumulation and the rate of charge flow is DC current by filter averaging).
All cables used for HV are tested by using PD impulse detection with the applied DC to determine the threshold of 1 pulse per minute or the inception threshold of PD. After this threshold the rep. rate quickly accelerates to 1 pps to 100 pps then to full conduction short. This applies to underground HVAC , HVDC and also your application.
Consider adding a series R to match the cable R to match impedances from a high Z MCP source mismatched to the cable Input capacitance (~<90 pF/m).
Consider cascaded stages of Av=1e4 max and cascaded glass butt-ended MCP’s for more gain with an ~ 10 deg offset to block returning noisy + ions with a gain from L/D ratio of about 50 of the clean glass channel.
Paschen’s Law will prevail in u-Torr vacuums ONLY if the surfaces are free of voids and contamination, so “cleanliness is godliness”.
BTW to see PD activity of <=1ns you need a LeCroy DSO scope, but you can hear it with an AM radio nearby tuned to a silent channel with volume turned up and will sound like any distant lightning.
I have never used an MCP, but have done a lot of PD testing at HV, if you need more assistance, reach out.