Ok, what follows is based on my experiences with "hardening off".
Leaves grown under weak florescent lighting will burn under direct sunlight. They don't "acclimate". They burn and die.
What you want is to place the young plants(as previously suggested) in a place that receives direct sunlight only late in the day, and/or early in the morning. After the plants have doubled in size, they can be safely placed in direct sunlight. The original leaves may die, but the new vegetation will be adapted.
I use a different technique, placing my seedlings in a greenhouse when I transplant them into one gallon pots. This prevents all burning when they go outside. Some stay in the greenhouses.
FYI, the T5s may be strong enough that the point is moot. The transition from T5s to sunlight may not cause burning. I'd put one plant out for a couple sunny days, and find out.