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I just bought my first RES yesterday. She is over 4" and is currently in a 20 gal aquarium although I do plan on upgrading.
I have a 4 year old son but the aquarium is out of his reach so he cannot handle the turtle.
I know the importance of proper hand washing before and after handling her and I do not
let her walk around on any surfaces in the house.
What are the chances of getting salmonella from her?

I think it's very low. A vast majority of kids getting salmonella from turtles is actually from directly playing with them, even putting smaller ones in their mouths. Also make sure you have an appropriate place to clean tank/filter equipment and are able to properly clean up.