If the district does not have an appropriate placement then you have the legal right to send him to a private school at district expense. They will likely fight you on it, but the squeaky wheel gets the grease.

Public schools for the most part cannot handle children on the spectrum or other disabilities. They do not have for the most part truly experience teachers or staff to work with the children of needs. The school will put together an IEP base on what the your doctor says and the school staff will do their best to accommodate your child's needs. The school's try to mainstream your child which is not good for your child because your child will not get the help he she needs to be at their best.
I am sure some public schools do better then others but it comes to a point where the staffing needs to no we don't have the mean to help your child and have that child transfer to a school that can work with your child but public schools don't want to pay for it so they keep changing the IEP to say they can work with your child and that process gives me a headache. At some point you may have to invest in an Educational attorney to have your child placed in the right school with the right program.

Many school systems put a lot of work into making sure that five-year-olds fit in based on their strengths. Meet with the school system and find out what they are able to do, specifically, to adjust and adapt.

It isn't really good enough to say "we can handle it." The school system needs to let you know what the plans are for potty time, what the plans are for teaching him to stand in line, what the plans are for getting him to sit down, what the plans are for dealing with meltdowns, and so on.

It is not unusual for a school system (these days) to be broke, so you may not be able to get as much speech therapy (for example) as you need. But it doesn't cost all that much to make plans, and a school system will function better if they have put their plans in writing.

You have to find out what the rules are in the state and the district because some of them do not let the teachers do much in the area of potty training or even helping the child in the bathroom at all.

As for just generally handling the child you have to find out what training the staff has or are required to have because generalized special Ed training will not cut it. Also I understand your concern about the child being non verbal and not knowing if something happened you would not know about it. That also comes down to the staff and how they are able to handle an ASD child.

Trust me you will know if something has happened because of how the child acts, it is a clear sign something happened if all of a sudden there is a change in attitude or behavior. If the staff has the training and you meet with them and they seem professional it should be ok. Also you can ask to sit in at first to watch how things go, they should accommodate the request and allow you to do it