how do i delete cities from Apple's Default weather app - or completely delete that app from my iPhone 5 S?

You cannot delete the Apple weather app. You can delete cities: click on the bottom right of the app. You will get a list of all the cities you have added. Swipe left on a city to delete a city. You can download any other weather app such as Yahoo weather. What is preventing you from doing this?

1. Be in list cities view (meaning viewing cities in horizontal rows)

2. Hold down your city until it moves and then swipe to the right and you will see 'Delete' option

William H. Magill1 wrote:

iPhone 5s - unable to delete cities from the list and cannot delete the app to replace it with one that works as it is an Apple default app.

That is correct. You cannot delete native iOS apps. What happens when you attempt to delete cities from the weather app? Do you have any restrictions on? If you tap on the small list icon in the bottom right of the screen, you will see a list of cities available in the app. From there, if you swipe to the left, you will see the option to delete.