Amom, just so you know, people with Autism are not "sick." It's not a mental illness.
As for the original question, you need to keep it simple. "Hayden did some naughty things/things he shouldn't do because he was having a bad day. You have bad days sometimes too, right? Remember the day you were so grumpy that you ____ and you got in trouble?"
Once you get her to empathize with him, then you can tell her, "When Hayden has bad days, it's not as easy for him to remember the rules as it is for you. That's because his brain works a little differently than yours. He feels things the same way, he likes to play like you do, but he thinks about things differently and remembers things differently. That doesn't mean he's a naughty boy. It just means that he needs some extra help sometimes, and a little extra understanding. There's a name for the way his brain works... it's called Autism."
As she gets older, you can answer her questions in more detail as is age appropriate. Let her ask questions, but this may satisfy her for now. Don't overload her.
Your daughter is at that prime age where she's a rule follower and she likes things neatly and in order... prime for entering kindergarten next year. But Hayden, even if he's the same age, is living in an extended toddlerhood and probably will be for several years due to having Autism. He's going to need more practice remembering rules, following rules, controlling his impulse control (which he has less of to begin with), and paying attention to how his actions affect others. Your daughter is learning all of these things on target, but Hayden is developmentally behind. All your daughter sees is his age and size.
My daughter comes against this too with children who haven't been with her in school since kindergarten or first grade. A lot of her classmates have been with her through preschool. They know she's different, they know she's special and they're protective of her even when she's a bit "naughty" but they don't know the name for why (most of them don't because of privacy laws, the teacher can't tell them, so unless I tell their parents or they grew up with her then they don't know it's ASD).
Anyway... please don't take this as a criticism, but take care to note when you speak about people WITH Autism. When you talk about someone being Autistic, it ought to be in the abstract but even then it's polite to refer to them as HAVING Autism.
The reason is because ASD is not the defining characteristic of someone. The disorder is not the person. The person HAS the disorder. You wouldn't say someone "is chicken pox" or "is depression" or "is Bi-Polar II." You would say that they "have chicken pox," "have depression," and "have Bi-Polar II." It's the same with Autism Spectrum Disorder.
It might be semantics, but it humanizes the disorder and personalizes it. It puts a face to ASD.