Will a iphone 5s from america work in australia?

Yes as they are global phones:)

If the phone is unlocked, you can use it in Australia with a supported GSM carrier. However, the LTE bands are not compatible and you will only get 3G speed. In addition, the iPhone warranty will only be valid in the US. If there's a problem with the phone, you will either need to bring the phone to the US yourself, or send it to someone you know in the US to bring the phone to Apple for service.

Hi, I have an iPhone 5S 1533 model and use in Colombia. I used this same model in Australia? What is the recommendation for these cases. Thank You.