That looks like fusarium mold, which has been a problem for many people in the east this year, probably because of all the rain. There have been several threads about it in the Allium forum. I would not plant those cloves. Clean bulbs from a coop or health food store would be better, regardless of type. I had a lot of suspicious bulbs in my hardnecks, so I dried them before the disease progressed. The softnecks were not as badly affected and are still looking perfect in storage.

It's all an experiment. I think that if you leave it in the garden, the bulbs will try to split and their cloves will be scrunched and won't form bulbs correctly, although they will try. Hopefully someone with better advice then mine will chime in but, I would carefully dig it up, split the cloves apart (with as little damage to the roots as possible) and replant immediately. I forget if you were concerned about disease or not. Although I have not seen diseases in my garden, I am determined to prevent them and I did trade/buy some this year...After a 2 week chilling, I soaked the popped cloves in a gallon of water that had a tablespoon each of baking soda and liquid seaweed. I used a plate to hold the cloves down, in a 5 gallon bucket. Then, I soaked the cloves in alcohol for a few minutes prior to planting.

What length and wattage T5? Without something in the photo to compare size with, those bulbs look like they might be T8. Anyway, you should use a fixture with reflectors.

I dug them up and then air dried them. Before this I never had any bugs bugging my garlic. I also made sure to start buying only organic garlic, as I had noticed a 'moldy' taste in the garlic at the store even though there was no mold on the cloves or even on the wrappers. I heard that the moldy tasting garlic is allegedly from China. The cloves looked perfectly normal, nothing else, but they all tasted moldy! Even after cooking! The organic garlic I buy doesn't have this problem.