TRICARE

Would it be advantageous for me to enroll in TRICARE (I am retired military) rather than remaining with my PSHB plan?

In general, TRICARE is a better choice than any PSHB plan, because its benefits are somewhat better and the premium costs far lower under all TRICARE options. But there are network differences that matter to some. You can "suspend" PSHB enrollment while in TRICARE just in case something changes and you want to reenroll.

Do I have to quit TRICARE and enroll in an PSHB plan for five years to meet the "five year rule" before retirement?

No, TRICARE service counts towards the five year rule. But you will have to be enrolled in an PSHB plan on the day you retire to keep PSHB as an option in retirement.