We have good data on thousands of children who have participated in the research studies, although it is true that follow-up in children has not been for as much time as adults.  This follows the usual vaccine process.  After you establish safety and efficacy in adults, you then move to teenagers and young adults, then older children, followed by younger children and infants.
Children ages 5-11 can get sick with COVID-19. Although most won’t be hospitalized or need the Intensive Care Unit (ICU), right now COVID-19 is the 8th leading cause of death in children. Sometimes they can get really sick. Children with COVID-19 are hospitalized all the time and require oxygen or breathing machines or even heart-lung support. This disease is preventable with vaccines and it’s important to know that thousands of children have gotten very sick already in the US alone. There is no way to predict who will get sick with more serious symptoms, although we do know that some children who have other medical conditions or who are overweight tend to get sicker.
In addition, children can spread the virus to their families and especially people like their grandparents, who are at even higher risk of serious disease or death due to COVID-19.  Right now, with the Delta variant of virus going around that is very contagious, it is much better to get your child immunized now rather than waiting.