The 5G series is quite old and not supported past, at the latest, ESXi 5.0.
Would it be better if I was to install ESXi 5.0?
For compatibility sake, yes, but use the HP customized ISO if you go down that route.
Where would I find this download for HP branded servers?
you can download from below link.
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HPE versions of ESXi will detect everything under the hood of your ProLiant, smart array controllers, fan and temp sensors, even iLO logs. HPE is a large dev partner and adopter of vmware.
I can confirm that HPE ESXI 5.5 will work on all ProLiant G5, and HPE ESXI 6.0U3 will work on your ProLiant G5 if the cpu allows it.
ESXi 6.0 does check the cpu on install and will stop if it doesn't pass. This exact info is on the compatibility lookup pages.