This is wrong, but admittedly by a very small margin.
The chance of finding a shiny in a horde is not equal to 5/4096, rather 1 - (4095/4096)^5. While this doesn't have a huge impact, it still is a calculation error. Same concept applies to the Shiny Charm.
I also admit, that the majority of people who read this will think that I'm off my rockers, but you need to cover basic probability first. ;>