Five years and billions of dollars ago, the problem seem surmountable. Yes, Lake Erie was dying. Yes, the Potamac was an open sewer. The streams and ponds and rivers and lakes in and around the nation's cities were unfishable, unswimmable and undrinkable.

But a technological society that sent man to the moon could surely clean up its own waste. In a spirit of brimming optimism, Congress passed the 1972 Federal Water Pollution Control Act.

Now the first clean-up deadline - July 1, 1977 - is upon us. Congress, the administration, industries, cities and environmentalists are gearing up to pick the law apart. Meanwhile, the average citizen might wonder: is the water getting any cleaner? The answer is: sort of.

Take the Hudson River Fashionable swimming resorts a few miles up from New York City were abandoned after World War II because of heavy industrial pollution. Oil and sewage killed most of the fish.

In the late 1960s, a vigorous anti-pollution campaign was undertaken, resulting in 160 new sewage plants. The 1972 federal law made industries install clean-up equipment, too. But, just as bluefish and crabs were returning to some parts of the river, a new hazard was discovered.

A dangerous chemical, polychlorinated biphenyls (PCBs), which cause nervous disorders and probably cancer and birth defects, had been discharged for years from two General Electric factories near Albany. An estimated 500,000 pounds of the almost indestructible compound now lie along a 50-mile stretch of the Hudson. Fishing was banned last year and the company has agreed to spend $3 million trying to clean up.

The Hudson is no isolated case. Just as the nation was beginning to congratulate itself - just as city mayors were holding press conferences to announce the catching of fish in their rivers - the problem of chemical pollution has come into public consciousness.

Industries, cities and the federal government have spent billions of dollars in the last five years building sophisticated plants to clean up pollution. But the equipment that destroys the bacteria in sewage water and the filters that collect solids and other conventional pollutants from industrial waste water are ineffective when it comes to manmade chemicals that, in minuscule amounts, are dangerous to human health.

When the 1972 act passed, the Environmental Protection Agency set up a massive, complex program. Guidelines wer issued for scores of different industries - from electroplating to sugar beet processing. Individual permits were required for 41,454 plants specifying how much each could discharge and what cleanup equipment was necessary.

By July, industries must install "best practicable technology," an interim cleanup standard that weighs costs and benefits. By 1983, the act requires "best available technology" - the best possbble equipment to make waters "fishable and swimmable."

Cleanup is expensive - the 1977 standards will end up costing industry an estimated $19 million - so hundreds of lawsuits were filed challenging the agency's guidelines and permits. Steel mills, power plants and oil refineries resisted regulation most strongly. But overall, about 90 per cent of industry is now in compliance.

Cities and towns, however, are way behind. By July 1, all 33,000 should have installed secondary sewage treatment - a process which removes 90 per cent of organic matter. The 1972 act provided $18 billion to fund 75 per cent of municipal plants - the largest public works program since the interstate highway system.

But fewer than half the country's cities and towns will comply with the deadline. Cities such as New York and Detroit are still dumping thousands of gallons of raw and almost untreated sewage into their rivers daily, while giant treatment plants are still on the drawing boards.

Grants were held up for several years when President Nixon impounded $9 billion, and, because of legal complications, the money finally being spent is spent inefficiently EPA officials say. Some cities are begging for money to build basic treatment plants while others have so much they are spending it on sewers, which they could afford to build with their own funds.

"An awful lot of gold-plated pipes are being installed," says Khristine G. Hall, a water pollution expert with the Natural Resources Defense Council.

At hearings this month, the Carter admininstration is expected to ask Congress to change the law to encourage faster municipal cleanup, and to shift from massive concrete treatment plants toward recycling plants that would use sewage water for irrigation. EPA may also ask for legal authority to force water conservation through such measure as shower head valves and toilet tank dams.

Even so, it could take 20 years for the nation's cities to meet the 1977 standards. Carter favors a $45 billion grant program spread over the next 10 years, but EPA estimates it could take another $87 billion to do the job.

And once the 1977 standards are finally met, would the water be clean? Unfortunately, no.

The government's water pollution program "has been geared to a past perception of the problem," said EPA's new assistant administrator, Thomas Jorling. "Since the early 1900s, we have concerned ourselves with basic sanitation - natural and human waste,. But now we have to change this mindset because we are in an industrial chemical era.

The nation, he said, has only recently become aware of chemical pollution. "If you don't look for something, you don't find it and we weren't looking for it," he said.

A suit by the Natural Resource Defense Council last year forced EPA to begin controlling fluid discharges of 65 toxic and heavy metals which are known to cause birth defects, cancer or acute illness. Now the agency will use the 1983 "best available technology" standards to try to control them.

Kepone in the James River, asbestos fibers in Lake Superior or cadmium, arsenic, chloroform, lead and vinyl chloride in waters across the country - these largely invisible threats "are more subtle, harder to diagnose and extremely difficult to control," Jorling said. "Like DDT, they tend to concentrate in the food chain" so that, while present in tiny amounts in the water, they accumulate in hazardous quantities in fish and animals, and even in mother's milk.

EPA has barely begun the task of finding out how much chemical pollution is out there and where it is located. But Jorling said that regulation of the first 65 - only a fraction of the 30,000 chemicals in commercial use - will affect almost every industry in the country.

And there is still another problem, if every industry controlled its discharges - biodegradable and chemical - and every town had secondary sewage treatment, the water still wouldn't be clean.

In the years since the water act, urban and agricultural runoff and natural drainage have been found to be the largest sources of water pollution. The Council on Environmental Quality estimated that in 1973, industry discharged 118 billion pounds and municipalites 6 billion pounds of solids into the nation's waters. By contrast, "non-point" sources - simple runoff - contributed 3,698 billion pounds.

When it rains in cities, the water washes into rivers carrying with it cadmium and carbon worn off automobiles tires, lead and other dirt from automobile exhausts and industrial smokestacks, and drainage from small businesses. EPA estimates it would cost $54 billion to build storm sewers that would carry thr runoff through municipal treatment plants instead of directly into rivers and lakes.

Agricutural runoff is even more difficult to control. Soil erosion is a major problem - 15 tons of topsoil flow out of the mouth of the Mississippi every second. Pesticides and fertilizers flow into lakes in irrigation water and run off into lakes and rivers where they poison the fish and stimulate choking algae growth. Cattle and hog excrement from feedlots cause more pollution than human sewage.

Section 208 of the water act calls for regional plans to control nonpoint pollution. But Jorling admits, "We're very far from coming up with any acceptable solution." Farmers and businessmen are worried regional plans will amount to restrictive federal land use.

As if this weren't controversy enough, the water act has spawned another issue that has Congress in a stew. After a lawsuit by environmentalists, the courts vastly expanded section 404 of the act by requiring the Army Corps of Engineers to issue permits for any destruction of wetlands in the nation.

Swaps and marshes protect water quality by absorbing pollution, but construction firms, farmers and private landowners are rebelling against federal control.

Thus cleaning up the nation's water has become, in the five years since the water act passed, a vastly more complex and controversial problem than was originally envisioned. In hearings this month, the Senate will grapple with the issue and probably draft significant revisions to the act.

The House, has already passed a bill granting more power to the states over municipal treatment and cutting back the wetlands protection. When the House tried to attach it to the jobs bill this spring, the Senate balked, setting the stage for a fight over comprehensive water pollution policy that is likely to last for at least a year.