Hello, I am trying to help someone out but this out of my normal area of work. The washing machine drains, overflowing the toilet about 15 feet away. About 10 days ago I snaked from the garage to the street, from the front of the house to the back and from the front to the street with a rented snake from home depot. 75 feet. All was draining but just started backing up again. I had read about running water down the exhaust from roof, that made the toilet overflow again. When I was moping up the floor the toilet did drain but very very slow. Ugh. Id like to help them. It's a small retirement home. Lots of soiled clothing and bedding to wash.
Thank you!

You still have a drainage problem between the toilet and the main sewer. When the washing machine drains it does not have enough flow to get rid of the waste water and therefore overflows the toilet. Call a professional plumber. This is not a job for amateurs. They will need some expensive equipment and someone who who knows what they are doing.

Since you say you have snaked every thing else you obviously know how to use a snake.

Pull the toilet and snake from there.