Use this interactive graphic from the Times-Picayune (the New Orleans area newspaper) to see.
Although New Orleans is below sea level, the city proper would not have flooded during a Category 5 hurricane had the levees held.
The breaches at the London Avenue, 17th St, and Industrial Canals were what caused most of the damage. These breaches were due to poor planning, execution, and construction materials. At the London Avenue Canal, for example, concrete floodwalls were put only 17′ into the soil despite the fact that the canal…
…is 18.5′ deep. The pressure at the bottom of the canal pushed the soft, sandy soil beneath the bottom of the concrete floodwall and pushed it upwards into the city. Similarly, a train had derailed in late 2004 and damaged a floodgate at the Industrial Canal. The repair was approximately $500,000, but the Army Corps of Engineers never spent the time or money to repair it.
Please keep in mind, to everyone in the New Orleans area (including Jefferson Parish, St. Bernard Parish, the Plaquemines, and the Lower 9th Ward), this was an engineering failure and a manmade disaster not an inevitability of Mother Nature.