Republican front-runner Donald Trump and Democratic rival Hillary Clinton sparred over the "woman card" and Sen. Bernie Sanders, after Trump won presidential primaries in five states and Clinton won four on April 26. (Sarah Parnass/The Washington Post)

Donald Trump won in all five Republican presidential primaries held on Tuesday — a clean sweep that illustrated his dominance along the Eastern Seaboard and prompted the real estate mogul to declare himself the “presumptive nominee.”

In the Democratic race, former secretary of state Hillary Clinton won four of the five states in play on Tuesday: Connecticut, Delaware, Maryland and Pennsylvania. Sen. Bernie Sanders (Vt.) won the primary in Rhode Island.

In both parties, those results extended the front-runner’s advantage in convention delegates.

Clinton appeared to have added 170 delegates to her lead over Sanders: By the Associated Press’s count, Clinton now has 88 percent of the delegates she needs to clinch the Democratic nomination.

In the GOP, Trump exceeded the already-high expectations for Tuesday. As of 10:55 p.m., the AP projected that Trump won at least 105 delegates, compared with just five for Ohio Gov. John Kasich and one for Sen. Ted Cruz (Tex.).

But the importance of Tuesday’s wins went beyond those numbers. For both Clinton and Trump, they showed that a long, drawn-out primary fight might be close to an end, and that stubborn adversaries seemed to be running out of time.

Clinton, speaking to supporters in Philadelphia, was not-very-subtly looking beyond the primary — attacking Trump, and making a pitch to Democrats to unite behind her.

“Whether you support Sen. Sanders or you support me, there’s much more that unites us than divides us,” Clinton said. She later talked about creating an America where “love trumps hate.” The crowd cheered at the pun, and a bumper sticker with the slogan was already on sale for $5 at Clinton’s website.

In the Republican race, Trump appeared to be trouncing his rivals by huge margins, winning by 30 percentage points or more in the first returns. Wins on that scale will make it harder for Cruz and Kasich to argue that Trump is a weak and divisive front-runner.

Neither of Trump’s rivals can possibly clinch the nomination before the GOP convention in Cleveland this summer. Both men are now relying on long-shot strategies, which imagine that Trump can also be stopped from reaching a majority of Republican delegates, and that the party’s convention will bypass the leader and choose one them instead.

“This is a lot bigger win than we would have expected. All five. And not only is it all five,” Trump said at a news conference at Trump Tower in New York. He noted that he had passed 60 percent in results from several states. “When you crack 60, with three people, that’s very hard to do. . . . That’s called a massive landslide.”

“I consider myself the presumptive nominee, absolutely. If you look. Honestly, Sen. Cruz and Gov. Kasich should really get out of the race. They have no path to victory at all. . . . We should heal the Republican Party, bring the Republican Party together. And I’m a unifier.”

Trump said he will be going to Indiana on Wednesday, where the May 3 primary is shaping up as the last best chance for Trump’s rivals to stop him. To help derail Trump, Kasich agreed this week to not campaign in Indiana, allowing Cruz to focus on the front-runner.

Trump had spent several weeks complaining that the GOP’s delegate system was rigged against him. On Tuesday, however, Trump was more ebullient.

“The best way to beat the system is to have evenings like this,” Trump said. He likened himself to a boxer, winning by knockout: “When the boxer knocks out the other boxer, you don’t have to wait around for a decision.”

Trump also tried to pivot toward a general election, although his attack on Clinton seemed more improvised that Clinton’s bumper-sticker-ready attack on him.

“If Hillary Clinton were a man, I don’t think she would get 5 percent of the vote,” he said.

Even before the polls closed Tuesday night, Cruz was conceding the expected losses, however, he showed no indication of withdrawing from the race.

“Tonight, Donald Trump is expected to have a good night,” he said, speaking to supporters in Knightstown, Ind., in the gym where the movie “Hoosiers” was filmed. (Cruz undercut his hoops credibility, however, by incorrectly forgetting the name of the hoop: He referred to it as a “basketball ring.”)

But then Cruz said that the race would turn his way, in states such as Indiana: “Tonight this campaign moves back to more favorable terrain.”

Kasich was running second in several of Tuesday’s primaries, but it was a distant second: hardly an affirmation of the theory that the governor would compete well with Trump among the more moderate Republicans of the East. It seemed likely that, even after Tuesday’s results were tallied, Kasich would still not have as many delegates as Sen. Marco Rubio (Fla.). Rubio dropped out of the presidential race more than a month ago.

In campaign parlance, Kasich was “down” on Tuesday night; he was back in Ohio and did not make a public statement or speech.

For Clinton, Tuesday’s victories in large, urban states reinforced her case against Sanders: that he has not broadened his coalition much beyond white liberals, and that he struggles to win urban areas and populous states.

Sanders, however, showed no signs of giving up.

The senator from Vermont appeared shortly after 8 p.m. to boisterous cheers in an arena in Huntington, W.Va., choosing to hold an election-night rally in a state that holds its primary in two weeks.

“This campaign is not just about electing a president. It is about transforming our nation,” Sanders said at the outset of his remarks to a crowd of about 6,400. “It is about having the courage to demand a political revolution, and you are the revolutionaries.”

Jose A. DelReal in Philadelphia, Katie Zezima in Washington, Abby Phillip in Hammond, Ind., David Weigel in McKees Rocks, Pa., Arelis R. Hernández in Fort Washington, Md., Sean Sullivan in Indianapolis, Katherine Shaver in Bethesda, Md., Josh Hicks in Annapolis, John Wagner in West Virginia, and Rachel Weiner and Ed O’Keefe in Washington contributed to this report.