Combine chicken, beans, tomatoes/chilis, lime juice, onion, garlic and spices in the slow cooker.
Whisk flour with 1 cup of water and add to the slow cooker.
Add the other 4 cups of water.
Cook on high for 4 hours (or medium for 6, low for 8) *To cook on the stove top, add an additional half cup of water, and simmer for an hour over low heat.
In a small sauce pan, whisk 3 Tbsp of cornstarch with 1/4 cup of water.
Once it's nicely mixed, add 1 cup of the liquid from the soup to the sauce pan and heat over medium heat. Once it starts to bubble, it will thicken right up very quickly.
Add it back to the soup and mix it in well with a spoon or the whisk.
Serve with crushed tortilla chips, cilantro, and sour cream.