O'Hare is my home airport. Unfortunately, this is could be a tricky connection for you without the shuttle running between terminal 3 and 5 (you didn't mention when you leave, perhaps it will be up and running again). Short version, if you are able to get on an earlier flight to get a longer layover, I would do so. Or see if you can switch to a flight operated by AA (but would be British Airways codeshare) which would leave out of Terminal 3.
If the people mover is up and running by then, it will be a bit better. But as a previous poster said, they have been working on that a couple of years. So you have to exit the airport and follow signs for the shuttle buses. You can get to them from the departures or arrival section of the airport. It would be at most a 12-15 minute walk, maybe faster depending on your pace and that is only if you are arriving on the furthest away gates. It could easily be a 5 minute walk. I think if you know you are looking for the signage for the shuttle buses, that will be more straightforward.
Security lines in terminal 5 are a nightmare. There are no TSA precheck lanes since these are all international airlines. If you are lucky enough to be flying business class, there are business class priority lanes.
If you walk out of the airport and there is a short taxi line, I agree to get in a taxi- more predictable and faster than the buses.
Good luck to you.