Knowing that lets us do a little math about expected death rates. In 2019, ~58,000 Scots died over the course of the year; that gives a rough chance of dying on any given day of 0.002%.
As of today, about 3m Scots are fully vaccinated vaccine, and another ~1m have either received a single dose or are still within the 2 week period after the second dose. If you add up the 28 day periods after those doses, that gives 196m days of Scots living "within 28 days of taking the 'vaccine'". You would then expect ~5,700 of them to die even if given saline, just by the underlying death rate.
So 5,500 is actually a bit lower than expected, maybe due to residual lockdown effect, or perhaps just that people who get vaccinated are generally better at risk/benefit analysis and are less likely to die from all causes.