Upgrading to vCenter 6.5
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There may be options using e.g. SRM, clustered databases, etc., but all of this comes with increased complexity. In addition to this, v5.5 is already out of support, so in case there's an issue (with, or without HA configuration), your basically alone.
Although you are asking for v5.5, I'd suggest that you rather consider upgrading to v6.5, which comes with integrated vCenter HA (in the vCSA).
If an upgrade is currently not al option, make sure that you do regular backups. In addition to this, storage based snapshots (if available) may also be an option for a fast recovery.