f5.6 is not a bad aperture, and unless you started opening the aperture up a lot more then chances are a busy background was going to happen with the cat so close to its background setting. As it is I feel that the exposure and lighting are very good and the body of the cat stands out well. You could try selectivly brightening the cats face a little bit (maybe darkening the background areas) just to try and bring his face out a little more.
I think the confusing thing about the shot is background areas on it look a bit like they are suffering from camera shake - which if course is totally offset by the sharp cat.
Monkey shot is cute - maybe consider cropping abit of the right so that he is looking into the left side of the frame a little more?
Good shooting in both cases though