I would be very careful what you discuss with your employer when it comes to a disability or a chronic illness. Most states are "At Will" states, which means, that they can let you go for whatever reason they want, as long as they don't discriminate.
As a private company, they can make up any company policy they please, as long as they do not break local, state, or federal laws. If there is no law regarding how many sick days is too many, then they can set it at 5. It is their company.
Now, if you have documentation of a disability, then your employer needs to know this. You have to follow the federal law regarding the defintion of disability. (This isn't something that your doctor can write on a script pad and expect your employer to accept it.) This will require your employer to make "reasonable accomodations" for you. That means, that if you are a waitress, and you have a lifting restriction of 10 pounds, then your employer would have to find another way for you to not have to lift anything over 10 pounds....as long as it is "reasonable". If there is a position available in the same company that wouldn't require you to lift anything, maybe as a hostess, then you might be a good fit for that. They company is not required to put you in that position, especially if they have to move someone out of it. The company may try for a while trying to make "reasonable accomodations", but it may get to a point where that is no longer feasible, and then they will be able to let you go because of an illness/injury/disability. Be extremely careful if you do have restrictions because if you get hurt while working and you break that restriction, you not only may not be covered by work comp, but it will give the company the power to let you go on the spot.