I became really ill about 3 months ago and spent over a month in the hospital. I have since been on disablility due to not being able to work. I called my apartment complex and told them my situation, it is a reoccuring illness and I have had to stay with my mom because I have not been able to take care of myself. They want me to pay almost $5000 to get out of my lease. Is there any way that I can get out of it legally? I need to move in with my mother due to not being able to work..

Often, no, but you will depend on the exact terms of the lease and where you live, ( if in the US each state has its own laws)

What is the rules on lease as to ability to sub lease it out

Given your health, I would hire a lawyer to help you. The lawyer will cost a lot less than $5000 and can probably negotiate a lower payment.

Is some of that money unpaid rent?

I would try and contact an ADA lawyer