System Manager (sysmgr), Persistent Storage Service (PSS), and Message & Transaction Services (MTS) are three major mechanisms supporting Nexus High Availability. They apply to any Nexus platform (well at least N7K/N5K/1000v) with some variation due to platform differences.
Sysmgr manages processes similar to linux "init". Processes can be restarted for various reasons (crash, memory threshold exceeded, not responding etc). Depending on policy and failure scenario the action may be to restart the chassis or switchover to the other Supervisor (N7K) or VSM (1000v).
PSS is a persistent database that any process can write to. What and how often depends on the process but the general idea is to update the data during steady state. Data can then be read back into the process after process restart, ISSU, or system restart.
MTS is the NX-OS Inter-Process Communication mechanism, similar to UNIX IPC but adds message persistence (survives process restarts) to support HA among other things.
Maybe an oversimplification, but all this applies to N5K minus the Sup/VSM switchover aspect. The following commands might not be 100% useful to you but you can at least see your 5500s have the same "HA plumbing".
show system internal sysmgr <options>
show system internal mts <options>
show system internal pss <options>