Would it be advantageous for me to enroll in TRICARE (I am retired military) rather than remaining with my FEHB plan?
In general, TRICARE is a better choice than any FEHB 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" FEHB enrollment while in TRICARE just in case something changes and you want to reenroll.
Do I have to quit TRICARE and enroll in an FEHB 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 FEHB plan on the day you retire to keep FEHB as an option in retirement.
I rely on TRICARE for most of my health care, but also want to stay in the FEHB program. What plan would be best?
To save money, you should consider switching to NALC Value Plan since its premium is so low. There is no less expensive plan. You wouldn't be able to use its personal health account since with TRICARE the FEHB plan would be primary and use up that account, but you would still be money ahead.