"over half a million people within 5 miles of my house" is more people and more densely populated than many cities though, so it seems a little silly not to call it one. There is only one city in my country with more people than that, and it's not as dense.

In many countries 'city' is a formal thing, and not related to the number of people living there. The smallest city in the UK has 1,797 people, and the largest town has 466,266 people, for example.