That's so sad!! My hearing girl is 5 and even if we can communicate easily, I'd bet if I sent her to live in a dorm she would think exactly the same: that I dropped her. No matter how much you explain, they're just too small... Days, weeks, are still hard to imagine. You can tell them "I'll come in a few days" but they'll still look for you when it's time to bed, they'll still miss you every day, they'll still think "what did I do so wrong that mum doesn't want me anymore?". So maybe she knows some sign, but... That may just not be enough for a 5 yo to accept such a separation.
That doesn't make it less strange anyway: if the son has used ASL since 1 yo, by 5 he could be able to teach many signs to his mother. I feel like this may be a case of lack of "bonding" between mother and child... And that is always so very sad! Luckily he found a welcoming environment in the deaf school... I hope she takes the chance to learn ASL now. The will to buy a bike at least shows us that she cares, and she feels something is missing between them: maybe in time she'll eventually find out what it is, and learn how to improve communications with her son. The school could help her in that sense.