Many people are reporting issues with the vCenter Server Appliance part of vSphere 6.5. Like ‘503 Service Unavailable’.
Anton Spiteri describes the issue here.
To make a long story short: this issue most likely is related to storage issues. VCSA is very sensitive to latency of the storage system it runs on. I experienced myself a vCenter appliance which entered an emergency state after a reboot. By fixing the disk I was able to get the VCSA up and running again. This blogpost explains how.
VCSA rebooted after one of my co-workers deployed a new virtual machine having a rather large disk installed on the same storage. In my case the storage was part of a temporary environment running Windows Server 2012 with a NFS export.
This post explains that increasing the SCSI timeout solves the issues.
A better option would be to upgrade the VCSA to 6.5 U1a.
Update 1a contains some critical security updates.