Scott has put a logical qualifier into the original question: why have you picked the five you picked, and what have you already played, so I'll start by stating that I've played Cypress, TOC, Pebble Beach and Sand Hills, which would all surely be on my Top Five if I hadn't been fortunate enough to play them already.
My remaining five would be:
1. Pine Valley. Reputed to be the best in the world by many; how can you fairly assess your other golf experiences if you haven't played Number One?
2. August National. I've walked it, and watched it hundreds of times. Who doesn't wonder what they'd do there with a club in their hands?
3. Royal County Down. This will stand in for all the Irish/Scottish courses I dearly want to play. I would make every effort to play Dornoch, Carnoustie, North Berwick, Muirfield and Turnberry if I return to Scotland, and Ballybunion, Portrush and Lahinch if I ever get to Ireland/N.I.
4. Seminole. The combination of Ross, Hogan, the Florida coastline and the ultra-exclusivity has always intrigued me.
5. NGLA (with a Shinnecock chaser.) I want to see CBM's laboratory, and play his versions of Scotland's greatest transplanted holes. Then I want to go next door see America's ultimate linksland course.
If I ever make it to these courses, I'd feel I'd done my best to educate myself as a golfer.