A record 5.3 million American families with low incomes have been bypassed by the booming economy and face a crisis of unaffordable rent, according to a report issued Tuesday by Housing Secretary Andrew Cuomo.

Cuomo will try to use the report's findings to persuade Congress to approve President Clinton's pending budget request for hundreds of millions of dollars in additional housing assistance."The report makes it clear that the federal government must significantly enhance its efforts to create more affordable housing opportunities," Cuomo said. "The strong economy that has brought prosperity to millions of Americans has not reduced the affordable housing crisis for millions of others."

The Department of Housing and Urban Renewal's report found:

- While the overall U.S. economy was good and getting better, American households with acute housing needs grew by nearly 400,000 over five years to 5.3 million in 1995. It has held steady thereafter.

- The number of affordable apartments for people with very low incomes fell by 900,000 from 1993 to 1995.

- The number of poor, working families needing housing assistance increased by 265,000, or 24 percent, from 1991 to 1995.