Investors cheered news of the deal and pushed Facebook shares up 1.8 per cent, while several powerful Democratic politicians in Washington condemned the proposed penalty as inadequate.
The FTC is expected to include in the settlement other restrictions on how Facebook treats user privacy, according to the Wall Street Journal.
The settlement would be the largest civil penalty ever paid to the agency.
Representative David Cicilline, a Democrat and chair of a congressional antitrust panel, called the $5 billion penalty "a Christmas present five months early."
"This fine is a fraction of Facebook's annual revenue. It won't make them think twice about their responsibility to protect user data," he said.
Facebook's revenue for the first quarter of this year was $US15.1 billion while its net income was $US2.43 billion. It would have been higher, but Facebook set aside $US3 billion for the FTC penalty.
While the deal resolves a major regulatory headache for Facebook, the Silicon Valley firm still faces further potential antitrust probes as the FTC and Justice Department undertake a wide-ranging review of competition among the biggest US tech companies.
It is also facing public criticism from President Donald Trump and others about its planned cryptocurrency Libra over concerns about privacy and money laundering.
The Cambridge Analytica missteps, as well as anger over hate speech and misinformation on its platform, have also prompted calls from people ranging from presidential candidate Senator Elizabeth Warren to a Facebook co-founder, Chris Hughes, for the government to force the social media giant to sell Instagram, which it bought in 2012, and WhatsApp, purchased in 2014.
But the company's core business has proven resilient, as Facebook blew past earnings estimates in the past two quarters.