More than 5 million children ages 10 and under--well below Facebook’s minimum age of 13--use the service, Consumer Reports has found in its 2011 State of the Net Survey.

The survey, included in our just-released report, also found that those kids’ Facebook accounts were largely unsupervised by their parents, exposing the children to malware or serious threats such as predators or bullies.

The report found that at least 7.5 million children—more than one-third of the 20 million minors who actively used Facebook in the past year—were under 13 and violated the site’s terms, which prohibit kids that young from joining.

The full survey results and advice for parents of Facebook users, is featured in the report, the June issue of Consumer Reports, and at ConsumerReports.org.