We have Big IP 8900 LTM with version 11.5.1. Is that compatible with PeopleSoft HCM & FSCM 9.2, PeopleTools version 8.54?

We're still 9.1/8.53 with 11.6.0, so I can't say for certain. The one thing I'd watch for is the use of WebSocket for the notifications in the new Fluid UI. A quick search says you can make that work in 11.5+ with an iRule.