I take my 3 year old to ATA. It is not Karate but Tae Kwon Do.(sp?) It is new and is at the corner of 55th and Willow Springs. I have mixed feelings about it. We have had three instructors so far - the best is the owner, Keith Shoup. My son is very high energy and has trouble keeping focused on the class (typical three year old). I would think a 5 year old would get much more out of the classes. Since it is new - there are not a lot of people in the class (more individual instruction) and it is reasonably priced. 3/4 are taught seperately - 5 year old are in a different class. I am not sure how much my son is learning though and just recently he has started saying he doesn't want to go back. You usually prepay for six months at these places.
We also took him to Blackbelt Academy on Ogden, also Tae Kwon do (Master Kim) just west of 83. It was much more serious - my son actually did really well in the trial classes and really liked it. 4-5 and maybe 6 year olds are put together - and there is an interview to make sure your child is ready. 3 year olds are not usually in the class. There were about 12 kids in the class, it was very structured, and the kids were really good so they were obviously learning something. Unfortunately it was very expensive (@ 230/month) which was out of our budget at this point especially since we didn't know if he would like it.
Hinsdale park district has Karate classes for 5 year olds too. You might want to check that out on their online site. That is actually Karate and not Tae Kwon Do.
Good luck,
H.