Experts and BHG readers answer.
The best time to move bulbs is after they have completely died down in the spring. If you move them when they are still growing, you'll disrupt their natural cycle of building up strength for another year of bloom. Keep in mind, though, that most tulips (except species types) generally don't bloom well after the first few years so I would suggest just planting new ones in the fall and not bothering to transplant. At 5 years of age, those bulbs are probably not worth moving.