(CNN) Two women from Hawaii who were lost at sea for nearly five months have been rescued by the US Navy.

Jennifer Appel, Tasha Fuiava and their two dogs were found Wednesday, drifting about 900 miles southeast of Japan, a Navy statement said.

"It was incredibly emotional and it was so satisfying to know the men and women that serve our country would come and assist us," Appel said in a call with the media Thursday. "It was actually quite mind-blowing and incredibly humbling."

Appel described the situation prior to the rescue as "very depressing" and "very hopeless."

"When I saw the gray boat on the edge of the horizon, my heart leapt because I knew we were about to be saved," she told NBC News . "Because I honestly believed we were going to die within the next 24 hours."

USS Ashland Command Master Chief Gary Wise welcomes aboard Jennifer Appel.

The pair left Hawaii on May 3 on the Sea Nymph, bound for Tahiti, about 2,600 miles way. They ran into trouble on May 30 when bad weather flooded the engine with water, Appel said. The women decided to keep sailing, but strayed off course, according to the Navy.

The ship's mast was also damaged, compromising the structural integrity, and limiting the Sea Nymph's capabilities to maneuver, Appel said in the call, obtained through CNN affiliate KHNL/KGMB.

Then the ship lost its communications capabilities.

After two months -- past the time they estimated they would arrive in Tahiti -- the Honolulu residents began sending out daily distress calls, the Navy said. But they were too far away from other boats and shore stations to be heard.

"You can't get any help at all because you're in the middle of nowhere," Fuiava said.

Appel and Fuiava survived on a year's worth of dry goods, including oatmeal, pasta and rice, the Navy said. They also had a water purifier.

The pair, along with their dogs -- or the "boys," as they call them -- survived two separate shark attacks, they said.

"And both of them -- we actually thought it was lights out," Appel said, "and they were horrific."

The first occurred one night when the Sea Nymph drifted into a pack of tiger sharks, Appel said. The next night, another came and slammed itself against the ship's hull.

"We were just incredibly lucky that our hull was strong enough to withstand the onslaught."

"There is a true humility to wondering if today is your last day," Appel added. "If tonight is your last night. If the storm that's approaching is going to bring down the rig."

'Thank God we've been rescued'

For 98 days, they sent distress signals, Appel and Fuiava said, hoping to be rescued.

After nearly five months lost at sea, they were finally spotted by a Taiwanese fishing vessel. The fishermen attempted to tow the sailboat, but when they failed, contacted the US Coast Guard.

The Navy discovered the boat Tuesday, about 900 miles southeast of Japan -- which is thousands of miles away from Tahiti.

Tasha Fuiava climbs to board the Ashland.

The USS Ashland, a ship based in Sasebo, Japan, was near the area on routine deployment and reached the damaged sailboat Wednesday morning.

"The US Navy is postured to assist any distressed mariner of any nationality during any type of situation," said Cmdr. Steven Wasson, Ashland commanding officer.

The Navy released video footage of the rescuers reaching the stricken sailboat. An ecstatic woman greeted them and blew kisses, while the two dogs, Zeus and Valentine, wearing bright, yellow life jackets, barked excitedly.

'Lucky to be alive'

It was a good thing the fishermen located the sailboat when and where they did, said Curtis Ebbesmeyer, a flotsam expert who co-wrote a book on the subject

The circular currents that carried the boat toward Japan could easily have sent it away from land, he said.

"If they hadn't been found there (off Japan) there's a good chance they'd have gone back out to the Pacific," Ebbesmeyer said. "The North Pacific is a really rough ocean in the winter. ... They're lucky to be alive."

He said flotsam and boats usually drift an average of 20 miles daily in the ocean. The distance and direction the women's sailboat covered was "a normal drift pattern," assuming it started drifting north of the equator, he said.

The women were smart to pack the water purifier, he said.

'You're around for a reason'

The sailboat was deemed unseaworthy and is currently drifting out at sea, a Navy spokesman said during the call from the Ashland.

The women were given medical assessments and will remain aboard the USS Ashland until its next port of call, the Navy said.

"I'm grateful for their service to our country," Appel said in a Navy statement. "They saved our lives. The pride and smiles we had when we saw [the US Navy] on the horizon was pure relief."

Sailors help Zeus, one of two dogs who were on the sailboat, aboard the Ashland.

Appel and Fuiava said they had no option but to carry on, so they tried to make the most of their time lost at sea.

"There's different sunrises and sunsets every day," Fuiava said. "And you're around for a reason, but you may as well use the time to do something beneficial."

Appel, Fuiava, Zeus and Valentine are safe with the US Navy. But The Sea Nymph is still out there, drifting.