I'm pro vaccine, and am convinced that the benefits of the vaccine absolutely eclipse the risks, but your math is so horrendously wrong here. Delete this.

Edit, here's some corrections:

This isn't 5 people in a row who had issues, it's 5 people within 4 nodes of distance in their social network. 4 nodes of distance is a lot of people, probably around 200,000 - 2,000,000.

The odds of having severe complications from the vaccine are about 1 in 100,000.

Therefore, everyone should expect to have 2-20 people within 4 nodes of their social network to have severe complications from the vaccine.

The mistake is not realizing the absolutely massive amount of people within 4 nodes of distance in your social network.

The other massive issue I see here is that there should also be somewhere around 500 covid deaths in the same pool of people that produced these 5 people with vaccine complications. The fact that they are focused on the 5 and not the 500 speaks heavily to their biases.

Keep in mind, all of this also assumes that what they're saying is 100% accurate, and these complications were definitely caused by the vaccine, and were not a coincidence. In truth, for every 1 person that has complications with the vaccine, 10-100x had the unlucky coincidence of something bad occurring that would have happened even if they hadn't gotten the vaccine.