I have had 93 Dialga encounters since the shiny became available, but only have one shiny. The odds of this happening with a 5% shiny rate are 0.9%.
Because I traded all Dialga from last year each one counts as two in my Pokédex, and I know that I only did one Dialga raid before the shiny was released, so I subtracted the number of recent Dialga that are untraded and the one from before the shiny was released, (143-42) and divided the answer (101) by two to get the number of Dialga that I caught + traded, and because there can’t be half of a Dialga it gets rounded to 51. Add the number of untraded Dialga, excluding the one from before shiny, to the number of traded Dialga to get 93 Dialga encounters.
Multiply the odds of not getting a shiny (0.95, with 1.00 equaling 100%) by the number of encounters minus 1 because of the ONE shiny, to get the odds of getting only one in 93 encounters (0.95 to the power of 92), which equals 0.008924, or a 0.9%, not 9%, but 0.9% chance of this happening.
While it is scientifically possible for this to happen, and would likely happen to one or two people if every player encountered this many, it seems unlikely that the chance has actually been 5% for a shiny.
Edit: all Dialga from 2021 were transferred after being traded, the Dialga from 2019 is untraded, and I didn’t do Go Fest 2020, so I don’t have any Dialga from that time.