First thing, you should not work in pixel in Illustrator, “inch” is the universal print unit and is a good choice since you want to print. Trying to convert inches to pixel seems to be a non sense to me while converting inches (or millimetres) to inches (or millimetres) is the way to go.
Second thing: Do not scale.
A good way to always get the good size is to use the ai export “preserve model scale” option and to avoid any scaling within Rhino.
Depending on the type of objects to deal with (furniture, truck, boat, yacht, building)… One little calculation to get the perfect ratio between illustrator and rhino layouts and voila.
In your case your layout is 5 inches x 5 inches and is a small object and 1 inch = 1 inch will give the good result.
Third thing: move the 0,0 point to the base of your drawing, this way it should stay within the illustrator workspace. Or use the command export with origin and set the origin to one of your object corners