iPhone 5s camera takes random size photos
Here is a logical explanation for the problem and although, I can't guarantee, in this case it is the problem, I think there is a high probability. 

When you select to email a photo, after you tap send, you are prompted with sizing (compression) options like this:



You can choose one of the options and as most things in life, everything has a trade off. If you select anything but "Actual Size", it will compress your photo, and the size it then comes in at will be smaller than what you would have expected. "Actual Size" is massive on all but the older iPhones. Full size it big, but likely will fit on a monitor, and the "Medium" and "Small" sizes are just like you described. 

This is not "lossless" compression like you see sometimes and does what it needs to with the image to reduce the actual file size.

For transferring images to your computer, AirDrop is the easiest way but only works if you have a Mac. If you use a PC, you could consider using iCloud for Windows to download Photostream images (which should be quite high resolution, if not natural size), or there is always the old faithful Image Capture