Hi and welcome to iMore.
The below is merely my opinion and I am not claiming it as fact.
I have an iPhone 5 and a Samsung Galaxy Note 3 and out of the two, the iPhone is by far the most reliable, in my experience. The Samsung is a fine phone but in my opinion the iPhone is just better.
If you need a larger screen then the SGS5 will be a great phone for you. It will do everything you want from it, going by your post above.
I think you will be happy with both devices but bear in mind that as Android has to work across many different devices, with a multitude of processors, RAM, screen sizes and configurations, I believe it will always be slightly less stable than iOS.