if you also use the vCenter you have to first update it before you update the esx server.
Dl385 g7 is supported up to esxi 6.0:
if this is a productive environment i would not update to 6.0. there are still a lot of bugs. i would go with 5.5
i would first update the esxi software and then update the firmware...
Thanks for adding your points: brunoferandez1
I would recommend to download latest ESXi 5.5 version [OR] Use HP OEM Image (based on your customer policies)
ESXi 5.5 Express Patch 6 2015-02-05
You can first plan for firmware upgrade - and download HP Customized ESXi 5.5 image which covers all latest drivers
This will help you to perform clean upgrade.