The FCA fined the five banks a total of £1.1bn, the largest fine imposed by it or its predecessor, the Financial Services Authority.
"At the heart of today's action is our finding that the failings at these banks undermine confidence in the UK financial system and put its integrity at risk," the FCA said.
The US regulator, the Commodity Futures Trading Commission, has fined the same banks a total of more than $1.4bn (£900m).
"The setting of a benchmark rate is not simply another opportunity for banks to earn a profit. Countless individuals and companies around the world rely on these rates to settle financial contracts," said the CFTC's director of enforcement Aitan Goelman.
The CFTC said its investigation found certain foreign exchange traders at the banks had coordinated their trading with traders at other banks to attempt to manipulate benchmark foreign exchange rates.
It said they had used private online chat rooms to communicate with one another.
The FCA said it had worked closely with the CFTC and other regulators in the US, Europe and the UK in issuing the fines, and said it was the first time it had pursued a settlement with a group of banks in this way.
"Today's fine marks the gravity of the failings we found and firms need to take responsibility for putting it right. They must make sure their traders do not game the system to boost profits or leave the ethics of their conduct to compliance to worry about," said FCA chief executive Martin Wheatley.
The failings occurred between 1 January 2008 and 15 October 2013, the FCA found.
The FCA said the banks had not "exercised adequate and effective control" over their foreign exchange trading businesses, training was "insufficient" and that the "right values and cultures" were not sufficiently embedded in the banks' foreign exchange businesses.
It found traders at different banks had formed "tight knit groups" to share information about client activity, using code names such as "the 3 musketeers", "the A-team" and "1 team, 1 dream" to describe the clients.