My recommendations are:
1) take a full backup of your database;
2) if running on virtual machine, take a snapshot;
3) make sure upgrade to a version that is supported by both versions (5.5 U3 and 6.x);---
Senior Infrastructure Specialist
This is the official documentation on preparing a Db before upgrading to vSphere 6.0. It contains some info about upgrading the DB before upgrading vCenter server.
I hope this solves your question.