Even now, five years on, Ray Nagin's words send a shiver down the spine. For the first time, a mayor was ordering the mandatory evacuation of New Orleans, as the winds that heralded the cataclysm began to howl through the streets. Hurricanes were embedded in city lore, but always, it seemed, the city dodged the bullet. Now however, that charmed life was about to end, Nagin warned on the morning of 28 August 2005, at the hands of "a storm that most of us have long feared".

That night, Hurricane Katrina duly smashed into the central Gulf Coast.

By many measures, Katrina was the worst disaster ever to befall the US. Beside it, the BP oil spill pales. More people – an estimated 8,000 – may have died in the Galveston hurricane of 1900, when modern communications and weather forecasting scarcely existed. And several more recent hurricanes have been fiercer, not least Camille, with its record winds of 190mph, which in 1969 followed a path close to Katrina's, but miraculously spared New Orleans.

But from Katrina there was no escape. The giant storm levelled virtually everything standing along 100 miles of coastline. In all, it killed 1,800 people in seven states, and caused $90bn (£58bn) of damage. It wreaked colossal damage on the region's oil, forestry and tourism industries. More than one million people were left homeless; the result, for a while, was the largest internal diaspora in American history.

But although swaths of Louisiana, Alabama and above all Mississippi were affected, Katrina is above all about New Orleans. Not since the San Francisco earthquake of 1906 has a great American city been so comprehensively devastated. At its height, four-fifths of New Orleans was under water, to a depth of 20 feet. Today, more than a quarter of the pre-Katrina population of 450,000 have not returned.

Books have been written and films made about the hurricane. President Barack Obama will be in New Orleans on 29 August, and a National Katrina Museum is due to open in a 12,000 sq ft warehouse in the Ninth Ward, the poorest and worst-hit part of the city. Special theatrical events are scheduled in New Orleans and around the country. Some anniversaries are empty ritual, but not this one. Five years later, the impact of Katrina is still being felt.

Storms are acts of nature, but Katrina's lethality was given a huge helping hand by human beings – even if you don't classify the hurricane as an "extreme weather event" directly caused by man-made global warming. In November 2009, a federal judge ruled that the US Army Corps of Engineers had displayed "gross negligence" in failing to maintain a navigation channel whose failure led to the flooding. The doctrine of "sovereign immunity" meant the Corps could not be sued – but the inundation was the most spectacular indictment imaginable of the ageing civil infrastructure that plagues the entire country.

Humans, moreover, had contributed to the disaster by destroying the Gulf wetlands that traditionally protected New Orleans, by blunting the storm surges that are the deadliest features of hurricanes. Katrina's main surge approached 25 feet, a veritable tsunami that overwhelmed the city's antiquated levees. And not least, the storm laid bare the inadequacies of government, and the shortcomings of a society unable or unwilling to protect its weakest members. Unsurprisingly, its political repercussions were vast and almost immediate.

No single event, not even the war in Iraq that was plainly unwinnable in the late summer of 2005, was as ruinous to the fortunes of George W Bush, who, just 10 months earlier, had narrowly defeated the Democrat John Kerry to win a second term in the White House.

Thereafter for Bush, it was downhill all the way. But it was Katrina that sealed the 43rd president's reputation for ineptitude, cronyism and near-complete disconnect from the reality of life for ordinary Americans, especially poor Americans – a reputation that remains.

Shortly after the disaster, Bush claimed that no one could have foreseen that New Orleans' levees would break; in fact, scientists had for years been warning the federal government of precisely such an eventuality, if a major hurricane scored a direct hit on New Orleans.

For days, he and his top aides seemed unable to grasp the magnitude of what had happened, despite the ever-more frantic appeals from state and city authorities, and the harrowing images on television. Everyone in America knew a disaster for the ages was unfolding – except, it seemed, the man in the White House (or rather, at that particular moment, at his holiday ranch in Texas). Not until the afternoon of 31 August, some 60 hours after Katrina struck, did the President take a first-hand look at the stricken city – but only from the window of Air Force One as it made a detour on its route back to Washington from his ranch in Texas.

When he did visit the Gulf Coast in person, two days later, the occasion was memorable only for two gaffes. One was Bush's expression of sympathy for Mississippi's Senator Trent Lott, who had lost his house in the storm. Its replacement would be "fantastic," the President burbled, "and I'm looking forward to sitting on the porch." All this as tens of thousands of poor blacks – their own far humbler porches either washed away or under 20 feet of water – were trying to stay alive amid the apocalypse that had engulfed them, just a few dozen miles away in New Orleans.

Even that tone-deaf remark paled, however, beside the praise he lavished on Michael Brown, the head of Fema, the federal disaster management agency, whose handling of the emergency had been a national disgrace. Brown, a former supervisor of horse show judges but with powerful friends in the administration, was utterly unqualified for the job – and performed accordingly.

Bush, though, seemed oblivious to the reality apparent to everyone else. "Brownie, you're doing a heck of a job," he declared, in a line that more than any other would define his presidency. A week later, Brown was fired, and in their minds, Americans did the same to their President. Before Katrina, people were still giving Bush a hearing. Thereafter, they simply tuned him out.

But the other ramifications of Katrina could not be tuned out. In the fetid waters that had taken over arguably its most beloved and distinctive city, the US saw a profoundly disturbing reflection of itself. The hurricane raised one uncomfortable question after another. How was it that an America able to send hundreds of thousands of troops halfway round the world to topple a dictator of whom it disapproved could not protect New Orleans? How could such a Third World disaster happen in the leader of the First World? Why did blacks suffer the most? Would the response have been as botched had a hurricane or earthquake struck Boston or San Francisco?

Maybe it would have been. "We felt we were written off by the government," a black New Orleanian reflected recently. "The real lesson is how cruelly we treat our citizens who have nothing. The middle classes, black and white, were able to leave New Orleans before the storm came. The people who couldn't afford to leave, they were on their own – and that about goes for any city in this country."

Or did "The Big Easy", fatalistic, frivolous and corrupt, simply get what was coming to it? In other words, was New Orleans – whose lack of preparedness for "the big one" was so brutally exposed by the shambles at the Superdome – as much to blame as the Bush administration? One question followed another. None could be easily answered.

Five years on, the hurricane's impact still reverberates in national, as well as local, politics. With the election in May of Mitch Landrieu, scion of the state's pre-eminent political family, to succeed Nagin, the city has its first white mayor since Mitch's father, Moon, left office in 1978. Paradoxically, the emigration of so many poor blacks to places such as Houston and Atlanta may have shifted the politics of both Louisiana and New Orleans to the right.

Nationally too, in a country with a notoriously short attention span, Katrina is not forgotten. The storm was the headline act of the exceptionally severe Atlantic hurricane season of 2005, that first helped to concentrate minds here on global warming. Three years later, the country elected its first black president, in what perhaps was an effort by voters to look beyond the enduring racial discrimination that Katrina had thrown into especially cruel relief.

Meanwhile, as they scramble to avoid a potential drubbing from Republicans in the midterm elections now barely two months off, Democrats are once again making the Bush legacy a central issue. Along with the wars in Iraq and Afghanistan, the recession and the deficit, the response to Katrina will also surely feature on the charge sheet.

Even more fundamentally, one must wonder whether Americans' lack of trust in the Washington establishment – the dominant theme of this political season, so vividly embodied in the Tea Party movement – stems, in part at least, from Katrina. When a section of the population needed the help of "big government" as rarely before in US history, the federal government establishment failed them.

In fact, much that is good has also happened in Katrina's aftermath. Fatalism breeds not just inertia but also resilience. Other places, faced with comparable catastrophe, might have simply thrown in the towel. Not, however, New Orleans. "We are veterans of pain," Mayor Landrieu told public television last month, in a documentary on the city's mood five years on.

But now fatalism has been joined by the demand that after decades of empty talk, the city at last tackles its age-old deficiencies. The truth is that New Orleans was losing population and business clout to places such as Houston and Atlanta well before Katrina struck. The storm merely accelerated that trend. If the city is serious about long-term recovery, it must do more than merely strengthen levees that crumbled and replace homes that were washed away.

The levees, we are told, have been fixed, and, albeit fitfully, the homes are being replaced. Many residential streets in the Lower Ninth Ward have been rebuilt, some with houses on stilts to protect against another inundation. Many, though, have not ben rebuilt. Rapidly they are being reclaimed by Mother Nature, who in the subtropical greenhouse of the Gulf Coast needs no second bidding.

Sometimes only a forlorn set of concrete steps protruding from the greenery marks where a house once stood, the paved road in front already pockmarked with clumps of weeds. Graffiti now covers the abandoned houses that did survive the storm, each bearing a faded waterline showing how high the Katrina flood reached.

But not just homes must be replaced. For all its magnetic allure, the city will not reclaim its vanished inhabitants until they are convinced that life will be better than on 27 August 2005. And that, above all, means better schools – with the result that New Orleans is now a laboratory for educational experiment closely watched by the US at large.

Across the city's poorer neighbourhoods, state-run schools were washed away along with the houses. These days, the public education system has only half as many students as before the hurricane, a sign of how young families above all decided to make a new life elsewhere.

But the system is now based on charter schools – publicly funded institutions that are managed independently, subject to specified performance targets. For now, at least, the experiment seems to be working: according to a 2010 report, 59 per cent of students are now in schools that meet state standards, against 28 per cent before the storm. The scheme's success is crucial. Only the certainty of decent public education will ensure the return of the missing middle-class black families, key to a resurgent New Orleans.

In one area, of course, it already is resurgent. Last February, the city's beloved Saints won the Super Bowl for the first time, defeating the Indianapolis Colts, watched in the US by 106 million people, the largest audience ever for a single television broadcast. In the most romantic fashion possible, the story of the Superdome, squalid shelter of last resort for the victims of Katrina, had come full-circle. For a year, the storm had forced the Saints from the city, as the arena was repaired. Now, they had reached the pinnacle of American football. No disrespect to the Indianapolis Colts, but the entire world beyond the state of Indiana was wanting a New Orleans victory.