You can put the T5 just about a couple inches from the plants, adding in some compact fluorescent lights wouldn't hurt. If the plant actually touches the bulb for any prolonged period of time it could still burn it. Even so, that lighting might only support a couple more weeks of any vigorous growth.
Now I can assure you that your plants are not growing because you are not watering them properly. They really need the water to support new growth. Don't worry so much about over-watering. That is something that happens from watering obsessively; when it really isn't necessary to because the soil is still moist. Plant roots need oxygen too, and when the soil is sopping wet all of the time it is difficult for the roots to obtain that's all.
Lift up your pots and you will feel how light they are...so water them good, until there is excess coming out of the drainage holes. You want to see run-off for a few reasons: it ensures you have watered thoroughly, you can collect it and check the pH and it also washes away salt accumulation. Afterward lift the pot and you will feel how heavy it is. When your pots are sufficiently heavy like that, you're all set. Now you wait a few days and lift them again, if they are about as light as that first time you lifted them; it is time to water. A second indicator is to check the first inch or so of soil. If that top soil is bone dry, then it is time to water.
You're not going to need to water very frequently at first. But, don't be surprised when your containers get lighter, quicker. As your plant develops more roots and foliage it will require more frequent watering (perhaps even daily), until it is time to transplant. After transplanting into a larger container you can typically go back to watering less frequently for a while.