bpk, willvan has already covered what went wrong with your direct posting of the images, so I won't comment on that.
I'm glad you are enjoying your S5200, it's a great camera which is seriously undervalued by those that don't share the experience of using one.
Your photos turned out very well indeed, and the AUTO setting works very well for static subjects & nice even lighting conditions. Using different settings probably wouldn't have improved them at all.
However, in other situations, it can be very worthwhile to switch it from AUTO to one of the other exposure modes. I'll give you 2 simple examples:
If you are shooting a fast action subject - say a sports event or motor racing, then it would be an advantage to select the S setting (Shutter Priority mode). This allows you to set a nice fast shutter speed of 1/500 or 1/1000 in order for the camera to be able to "freeze" the action without blurring. The camera automatically selects the required aperture (lens opening) required for the correct exposure. This mode is also useful when you zoom right in to the subject (at maximum zoom it is equivalent to 380mm in 35mm film camera terms). In this case you need to be able to select a nice fast shutter speed in order to avoid blurring caused by the camera moving as you take the shot.
In a different situation you may be taking a landscape where you want both the foreground & background to be in sharp focus (ie. a broad depth of field). In this case the A (Aperture Priority mode) is useful, because it allows you to manually choose a small aperture (bigger f number) which gives you the broad depth of field you are after. In this case, the camera then automatically selects the shutter speed to give the correct exposure. You just need to make sure that you are able to use a fast enough shutter speed to eliminate blurr from camera movement. The rule here is that you should use a shutter speed that is at least the inverse of the 35mm equivalent lens length. For example if you were about half way through the zoom range on the S5600, you would be taking a photo of the equivalent of about 200mm on a 35mm film camera (roughly half way between the wide angle end of 38mm & the telephoto end of 380mm). In this case you need to be using a shutter speed of at least 1/200 (1/500 even better) in order to help eliminate blurr.
The other worthwhile setting to try is the P (Program mode). In this mode, the camera suggests a range of combinations of shutter speed & aperture that will give you correct exposure, and you can scroll up & down to select the best combination for your type of photo. This is in some ways a better "automatic" setting than using AUTO because it allows you to manually set the other exposure variable, that is the ISO setting. Low ISO (light sensitivity) settings like 64, 80 or 100 give you the best quality images. However, when the lighting isn't very good, you may need to choose a higher ISO setting of say 400 or 800. However the downside of the higher ISO settings (particulary 1600) is that the image quality isn't as good. You get "noise" in the image - a grainy unsharp, flat looking image.
One other point is what image quality setting are you using. I think the 5MP Normal JPEG mode is the default setting on the S5600. You will find that you get better quality images using the 5MP Fine JPEG mode (although you will only fit half the number of images on your memory card).
Two final points - 1. Get out & take lots of photos & work out what you like, and what can go wrong using different settings, and 2. Keep reading the manual a bit at a time - it will explain the settings & how to change them.
Have fun!
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