(Video was recorded a few hours before cruise ship docked)

Passengers who finally escaped the disabled Carnival cruise ship Triumph have been checking into hotels for a hot shower, fresh-cooked food and sleep, or boarding buses for a long haul home after five numbing days at sea on a powerless ship.

The holiday ship carrying some 4,200 people docked in Mobile, Alabama, after a painfully slow approach that took most of the day. Passengers raucously cheered after days of what they described as overflowing toilets, food shortages and foul odours.

"Sweet Home Alabama!" read one of the homemade signs passengers affixed alongside the 14-storey ship as many celebrated at deck rails. The ship's horn loudly blasted several times as four tugboats pulled the crippled ship to shore. Some gave a thumbs-up sign.

Deborah Knight, 56, of Houston, had no interest in boarding one of about 100 buses assembled to carry passengers to hotels in New Orleans or Texas. Her husband Seth drove in from Houston and they checked into a Mobile hotel.

"I want a hot shower and a daggum Whataburger," she said. She said she was afraid to eat the food on board and was taken ill while on the ship.

Some got emotional as they described the deplorable conditions of the ship.

"It was horrible, just horrible" said Maria Hernandez, 28, of Angleton, Texas, as she talked about waking up to smoke in her lower-level room on Sunday and the days of heat and stench to follow. She was on a "girls trip" with friends.

She said the group hauled mattresses to upper-level decks to escape the heat. She managed a smile and even a giggle when asked to show her red "poo-poo bag" - distributed by the cruise line for collecting human waste.

In texts and mobile phone calls, the ship's passengers described miserable conditions while at sea.

The ill-fated ship lost power in an engine-room fire on Sunday some 150 miles (240 kms) off Mexico's Yucatan peninsula. It was the end of a cruise that wasn't anything like what a brochure might describe.

Carnival CEO Gerry Cahill apologised at a news conference and later on the public address system as people were disembarking.

"I appreciate the patience of our guests and their ability to cope with the situation. And I'd like to reiterate the apology I made earlier. I know the conditions on board were very poor," he said. "We pride ourselves on providing our guests with a great vacation experience, and clearly we failed in this particular case."

While the passengers are heading home, Triumph will head to a Mobile shipyard for assessment.

In a text message, Kalin Hill, of Houston, described deplorable conditions over the past few days.

"The lower decks had it the worst, the floors 'squish' when you walk and lots of the lower rooms have flooding from above floors," she wrote. "Half the bachelorette party was on two; the smell down there literally chokes you and hurts your eyes."

The company disputed the accounts of passengers who described the ship as filthy, saying employees were doing everything to ensure people were comfortable.

Carnival has cancelled a dozen more planned voyages aboard the Triumph and acknowledged the crippled ship had been plagued by other mechanical problems in the weeks before the engine-room blaze. The National Transportation Safety Board has opened an investigation.

Passengers were supposed to get a full refund and discounts on future cruises, and Carnival announced they would each get an additional 500 euros in compensation.

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