Think about your question this way. Instead of trying to think about having 5/3's of a bag of popcorn, simplify the fraction into a real-life manner. If you have 5/3 bags of popcorn, that means you are going to have 1 and 2/3 bags of popcorn. Now this is really easy to understand because now you only have to deal with the 2/3 full bag of popcorn. Since Jane ate 1/3 of the 2/3 full bag of popcorn, this means that Lillian has 1 and 1/3 bags of popcorn left. (Or this can also be written as 4/3 bag of popcorn)
Hope this helps! :)