The social network must also establish an independent privacy committee that Facebook's chief executive Mark Zuckerberg will not have control over.
The FTC had been probing allegations political consultancy Cambridge Analytica improperly obtained the data of up to 87 million Facebook users.
The probe then widened to include other issues such as facial recognition.
The $5bn fine is believed to be the biggest ever imposed on any company for violating consumers' privacy.
"Despite repeated promises to its billions of users worldwide that they could control how their personal information is shared, Facebook undermined consumers' choices," said FTC chairman Joe Simons.
He added that the heavy fine was designed "to change Facebook's entire privacy culture to decrease the likelihood of continued violations".
Facebook's financial results reported on Wednesday did not reflect any move by customers to shun the network over privacy concerns. It said monthly active users had risen 8% in the second quarter. Revenues, mainly advertising sales, rose by 28%, beating analysts' forecasts.