PHILADELPHIA — In a front-runner’s rout, Republican Donald Trump roared to victory Tuesday in five contests across the Northeast and confidently declared himself the GOP’s “presumptive nominee.” Hillary Clinton was dominant in four Democratic races and now is 90 percent of the way to the number she needs to claim her own nomination.

Trump’s and Clinton’s wins propelled them ever closer to a general election showdown. Still, Sanders and Republicans Ted Cruz and John Kasich, vowed to keep running, even as opportunities to topple the leaders dwindle.

Trump still must negotiate a narrow path to keep from falling short of the delegates needed to seal the nomination before the Republican National Convention in July. Cruz and Kasich are working toward that result, which would leave Trump open to a floor fight in which delegates could turn to someone else.

Trump was having none of that. “It’s over. As far as I’m concerned it’s over,” he declared at his victory rally in the lobby of Trump Tower in New York. He now has 77 percent of the delegates he needs.

With Clinton’s four victories — she ceded only Rhode Island to Vermont Sen. Bernie Sanders — she now has 90 percent of the delegates she needs to become the first woman nominated by a major party. Clinton kept her focus firmly on the general election as she spoke to supporters Tuesday night, urging Sanders’ loyal supporters to help her unify the Democratic Party and reaching out to GOP voters who may be unhappy with their party’s options.

“If you are a Democrat, an independent or a thoughtful Republican, you know that their approach is not going to build an America where we increase opportunity or decrease inequality,” Clinton said of the GOP candidates. She spoke in Philadelphia, where Democrats will gather in July for their nominating convention.

Sanders, in an interview with The Associated Press, conceded that he has a “very narrow path and we’re going to have to win some big victories.”

Trump’s victories in Maryland, Pennsylvania, Connecticut, Delaware and Rhode Island were overwhelming, winning his closest race by just about 30 points. The businessman is the only candidate left in the three-person race who could possibly clinch the nomination through the regular voting process. Yet with 950 delegates now, he could still fall short of the 1,237 he needs.

Cruz and Kasich are desperately trying to keep Trump from that magic number and push the race to a convention fight. The Texas senator and Ohio governor even took the rare step of announcing plans to coordinate in upcoming contests to try to minimize Trump’s delegate totals.