what exactly is your question? If your question is the title of your post then i would have to say that it looks like shell rot to me. Smell the areas where you see the lighter spots and if it smells bad, then its shell rot. There is lots of info on the website on how to treat shell rot. For minor cases, dry docking (meaning keeping your turt out of the water for a period of time) and gently pick loose pieces of fungus off with your finger nail. Then gently rub the infected areas with some povidone iodine and a soft bristled tooth brush. But again, this is for minor cases. Shell rot will usually not go away without treatment so you must act on this. If you find that those white spots pitted the shell and extend deep into the shell then you should really consult with a herp vet asap.
BTW
You need to add more water to that tank asap. It looks like you have maybe an inch of water in there. You should have it filled as high as possible without the turtle being able to climb out.
I have read everything there already and it did not really answer my question so here I am.
To me it looks like you dont have a sufficient set up at all for your turtle. Read everything again and you will realize what improvements you MUST make to your habitat. Take some time and read over the whole site (yeah it takes time but everyone here probably has done so atleast once)
Here's a list of things to get you started (this all can be found on the site)
-Aquarium with 10 gallons of water per inch of shell (5 inch turtle requires atleast 50 gallon aquarium or tub)
-UVB Bulb (overtop the basking area)
-Heat Lamp (any incadecent house lightbulb will do)
-A filter that pumps atleast 3-5x the amount of water in your tank per hour IE 30 gallon tank should require a pump that can turn over the water at about 90-150 gph.
-Water heater (water temp 73-80 degrees)
-Basking area with temps 10 degrees warmer than your water temp