95% effectiveness does not mean 5% of people had symptomatic infections. It means there were 20 times more infections in the placebo group compared to control.

If you gave the vaccine to 1000 people and placebo to 1000 people, and 100 of the placebo and 5 of the treatment group got sick, that's 95% effective, as is if all 1000 in the control group got COVID and only 50 in the treatment group.